Saturday, September 15, 2012

The Science of Photography -- Part Nine

In the last installment we discussed many different things, but the key topic was the resolution of film, which we found was very,very high compared to even the latest digital camera sensors. We also learned that film has a gradual loss of ability to record the highest details. This soft failure of resolution is quite different than the very specific limits of resolution with digital camera sensors. You will get no detail greater than the pixel count of the sensor. Further, the eye functions more like film. This may be why we find film photographs more pleasing to the eye and why digital photographers are always looking for “the film look.”

In this part we will learn how digital camera sensors are made, their limitations, and the various engineering tricks that have been polished to the “state-of-the-art” in order to provide maximum camera performance.

In the digital camera market the key performance indicator is typically the total number of pixels, measured in the millions: “megapixels.” Even the name, “mega,” screams advertising. It is a wonder of modern science and engineering just how many of these mega-things can be squeezed onto tiny sensors. So what is the importance of megapixels? Are they as irrelevant as horsepower has become in today’s automobile market place. Do megapixels really count?. And, just as horsepower typically is a trade off with fuel economy, are megapixels a trade-off too? What do we give up to get a high pixel count?

The answer to these and other questions will be answered in a few short, and maybe not so short, paragraphs. Read on.


The sensors used in digital cameras, from the cheapest point-and-shoot or smartphone camera to the sensor in a professional DSLR camera with a price that rivals the cost of a new automobile, are all pretty much made the same way. Regardless of whether the design is CCD or CMOS, a camera sensor is simply an integrated circuit; one originally designed as a form of memory storage. Today, CCD designs are only used for sensors, but CMOS is used as well for computer memory, processing, and other digital functions.

Charge Coupled Device, or CCD sensors were some of the earliest sensors developed. I’ve mentioned previously their use in early video cameras in the 50’s. CCDs, though eclipsed long ago for use as memory devices, and needing additional off-chip processing circuitry, are still in use at the high end of image capture, including in all medium format digital cameras. (Medium format is larger than 35mm but smaller than very large cameras like the 4” x 5” Press camera.)

The reason for this is their superior image quality. They have the potential for greater light sensitivity, lower noise, and higher dynamic range. This is not to say that there aren't CMOS cameras that are capable of very good, even excellent performance in these areas. But, one has to ask why companies like Phase One, Leaf, Hasselblad / Imacon, and various military and scientific applications prefer to use CCD chips, in spite of their higher costs, greater power needs, and other drawbacks. The answer likely comes down to one thing – image quality.

But for those of us with smaller budgets, consumers of point-and-shoot cameras and even pro-am DSLRs will find Complementary Metallic Oxide Semiconductor or CMOS sensors in our cameras.  CMOS has become the current mainstream of chip design. It is capable of incorporating a great many additional functions right on the chip, including analog to digital conversion (ADC) and other aspects of image processing. (Recall I mentioned earlier that these sensors are actually analog devices, so the output must be converted to a digital format, numbers consisting of zeros and ones. Hence the need for the ADC function on the sensor chip.)

Combined with the fact that more capabilities can be built right on to the chip, and the fact that the fabrication plants are used for chips found in many other contemporary silicon products, especially memory chips, CMOS designs are much less expensive to build. In combination with the higher circuit density allowed by integrating more functions on the chip, you end up with lower costs and smaller ultimate size, an important factor when used in small cameras, such as those in cell phones, for example. CMOS sensors also use less power than do CCDs. That improves camera battery life.

Imaging sensors come in different sizes, ranging from smaller than the head of a nail to the size of a saltine cracker to even bigger. A sensor chip's size is a key variable in determining its cost. Chips are made from silicon wafers. Whereas literally thousands of sensor chips, such as those used in a web cam, can be cut from a single wafer, only a handful of medium format chips can be derived from a standard 6"or 12" wafer. This means that their wholesale costs can range from less than a dollar, to several thousand dollars per finished chip.

The value of wafer real estate is just one factor in determining its cost. Rejection rate is another. A wafer with hundreds or even thousands of individual chips on it is tested, and only the chips that function properly are passed to the next manufacturing stage. The percentage of good chips on a wafer is called “yield.” With large chips, there is a greater opportunity for a defective area to be inside the boundary of the chip. With smaller chips, the probability is lower. For that reason alone, the yield is higher when manufacturing smaller chips out of a wafer of silicon.

With millions of components (diodes and transistors) on modern sensor chips, it's almost impossible with today's technology to make a perfect chip. Consequently both manufacturers and camera makers set their own criteria for whether a chip is usable or not. This will include the number of defective pixels as well as rows, and consecutive rows that are permitted. The nature of these criteria are closely held corporate secrets. Regardless, the conclusion is that the larger the sensor, the higher the wholesale cost to the camera manufacturer.

Sensor size has several effects on overall picture quality. First, the larger the sensor, the more light it will gather. Plus, the larger the captured image, the less the image has to be enlarged or “blown up” to reach a final usable size. Of course, this final usable size depends on what that use is. Is it to be sent over the internet, or displayed on a computer monitor? Or do we want to produce prints? What size prints? 4x5, or large wall hangings?

How much you can enlarge a digital photograph depends on the picture’s resolution. The maximum resolution you can obtain from a given digital camera is equal to the resolution of the picture sensor in the camera. And resolution is also related to the size of sensor. Obviously, the larger the sensor, the greater the number of individual sensors called pixels, that can be fit on the chip. The total number of pixels on a sensor is the “megapixel” measurement, the total count of pixels.

What is most interesting is how small sensors can have as many pixels or megapixels as a large sensor. Obviously, from the rules of geometry, to fit the same number of sensors on a smaller chip will require the size of the individual sensor to be smaller.

Pixel Size

Chip size and individual pixel size are factors which combine to determine not only a sensor's cost but also many aspects of its performance. More pixels means higher resolution. But having more pixels to record images means either putting more of them on a given chip size or making the chip bigger.

In the race to get high “mega” numbers, even small sensor chips are designed with a large number of these sensor sites. But, the only way to add more pixels to a chip of a given size is to make the pixels smaller. Further, as the pixels become smaller they are less able to capture photons (the discrete components of light), and therefore their signal to noise ratio decreases. All electronic circuits have inherent noise. The more signal (light) there is, the lower the noise is relative to that signal. In engineering we call this the signal to noise ratio or “S/N.”

You may have noticed, when listening to AM radio stations on you car radio, that strong stations sound fine, but weak stations seem to have a lot of noise or static. That is because the weak stations have to be amplified more in the radio circuitry. There are automatic level controls in the radio that adjust the amplifier gain based on signal strength. The greater the amplifier gain, the more noise introduced. That’s why digital cameras experience noise problems with low light. So this noise issue is tied directly to low light performance.

Camera “noise” is directly related to the size of the individual pixel sensors. We will measure something called “pixel pitch” which is the distance between the centers of adjacent pixels. It is a good approximation of the individual pixel diameters. We can assume that the individual pixel sensors can be packed together very tightly. In reality there is some space between sensors, but it is quite small, and we’ll ignore that.

As you compare pixel pitch between two cameras with the same megapixel count, but one, such as an inexpensive point-and-shoot camera, and the other an expensive DSLR camera with a APC or full size sensor and, obviously the larger sensor with the same number of pixels has larger individual pixel sensors. This results in greater sensitivity to light and lower noise in the image capture. If the sensor is not as sensitive to light, then the captured signal must be amplified more than with large sensor pixels.

This is why point-and-shoot cameras produce noisy images at high ISO settings, and why the Nikon D3 with its large pixel pitch (8.4 µm) has much lower noise at high ISO settings than a point-and-shoot that might have a pixel pitch as small as 1.7 µm.

So what is the optimum size for a pixel sensor? The size of a pixel directly impacts how much noise an image will have in low light, and in some cases even in daylight. The bigger the pixel is, the lower the noise because more photons can reach a bigger pixel sensor. But stating the optimum size value depends on the state of the art -- and that state is continually improving. Certainly, pixel pitch of 6-8 microns is very good, but smaller sensors and smaller pixel pitch sizes are continually improving. And, since smaller sensors work with smaller lenses, which can be made more precisely for less money, the total camera package could outperform larger sensor cameras.

Camera and sensor manufactures are both continually improving their products and a lot of powerful engineering goes into today’s products to let them perform better than what was sold just one year ago. At this point you can’t say what the optimum pixel sensor size is. It keeps getting smaller.

An example of just one of those state-of-the-art improvements is “backside illumination” used in the camera chip in the iPhone 4s. In order to increase the amount of light reaching the sensor on the latest iPhone, the image chip is actually mounted upside down. This is called backside illumination. (The chip isn’t so much “mounted upside down,” it is designed to allow it to be mounted upside down.) This puts the circuits, the small “wires” that connect the components on the bottom of the chip. They are normally on the top, getting in the way of light falling on the sensor. So backside illumination increases the total amount of light striking the sensor. This is one example of the engineering improvements that appear as sensor design improves.

So, again, what is the optimum size for a pixel sensor? This is a bit of a moving target. Chip makers and camera makers continue to improve their circuitry and noise reduction capabilities. But the laws of physics can't be denied. Plus, all technologies used to reduce noise on new designs of chips with smaller pixels can equally be applied to those with larger pixels. So while absolute improvements are being seen, relatively speaking the gap between them remains roughly the same.

As noise reduction and other improvements continue to be developed we expect to see continued increases in pixel density. However, all engineering improvements reach their limits, and we may be pretty near those limits now. The physics of light, itself, and the fact it comes in discrete packets called photons provides a lower limit to pixel pitch. So we will eventually see the smallest possible pixels and that will be the end of the road for size reduction.

Sensor Size

Now that we know about pixel size and the accompanying issues, we can make some sense of the entire situation of relative sensor size, image quality, and costs. Put simply, bigger is better, and costs more. That's the core of any discussion about digital image sensors.

The statement that bigger is better has implications for the competitive marketplace. In the days of film no one argued with the fact that large format (4” x 5” film) produced superior image quality to medium format (2-1/4” x 2-1/4” film), and that medium format offered higher image quality than 35mm, and so on down the line -- if you ignore the negative issues of large size such as camera weight and cost.

With digital many argue that as long as an image doesn't need to be enlarged beyond the resolving ability of the output medium (say, 300 dpi when making an inkjet print) there is no disadvantage to a smaller imaging chip. Well, maybe, but then, maybe not.

In my opinion, for most everyday camera uses, a resolution of 10-16 MP is probably adequate. Certainly 8MP cameras can perform pretty well, but when you get down below 5MP, you are starting to sacrifice quality. To illustrate this, the iPhone 3s only had a 3 MP camera. The iPhone 4 has a 5MP camera and is noticeably better, although some improvement is in the electronic processing and some is in a better lens. The iPhone 4s has an 8MP sensor, plus again the electronics was improved and the lens is now a sophisticated 5 element stack. I would argue that the current iPhone camera is about as good as you can expect from a fixed focus design.

On the high end of resolution, I don’t think there is a specific limit. As long as the total sensor area is large enough to support adequate sized pixels, the more resolution the greater the ability to enlarge the photo. I don’t know the upper limit for normal use. Certainly when enlarging a photo to fit on an entire wall, higher resolution is useful. But, then, how often do we need to enlarge a digital photography to eight feet tall? The digital sensor in a spy satellite would have little cost-consciousness and I expect no limit in the resolution goals of the government designing such high powered systems.

Further, we know from personal experience that you need to, at least, double the number of pixels to really get a significant improvement in the pictures, and some think the needed change is even greater, as much as a times four increase to see visible improvement. So there is probably little difference between a 12MP camera and a 16MP camera. It would probably take at least a 24MP sensor to show significant improvement over a 12MP camera, all else being equal. For all of these reasons, I think the MP race is probably over with 10-15MP as the sweet spot with cameras using small sensors.

I once saw a chart of all the various pixel pitches and there was a big gap between what we saw in the small sensor -- point-and-shoot cameras and the larger sensor, higher quality digital cameras such as the DSLRs. There are some good quality cameras in the market place with sensors smaller than the APC size. For example, the new Nikon CX and the smaller Panasonic and Olympus 4/3” sensors. I expect to see more quality cameras using those size sensors and benefiting from the small size and lower weight of an overall design matching these sensors. But, for the high depth of field effects that you can obtain from a full format camera and the higher resolution and low noise performance of full 35mm sensors (and even larger), the simple physics will always give these larger format sensors the edge -- albeit at the expense of size and weight -- as well as at the expense of dollars to purchase the camera and compatible lenses.

There are so many different situations and variables that I’m not ready to state a particular best pixel count, but I have noted some new camera models actually have lower megapixel counts than the previous model. However, people are still impressed by the number of pixels, so it is hard to determine in more pixels are for better photographs, or just to sell more cameras. In photography, the basic rule of physics applies: “You get what you pay for!”

What it is that we're seeing is these higher resolution photos is another matter. It can be called  micro-contrast; very fine tonal transitions that seems to get lost with smaller size sensors. This could well be caused by the relative lack of strain on the camera's lens design when lower magnifications are called for. It is also something that we've always seen when comparing larger formats to smaller ones in the film world. I will discuss methods to measure this small detail sensitivity in a future article when I describe the Modulation Transfer Function, a precise method to measure resolution with images. The final measure is a combination of sensor and lens and light and several other factors.

So, regardless of advances in engineering, the fact remains that physically larger sensors will always have an advantages over smaller ones. This means that (other factors aside) image quality from medium format cameras (2-1/4” x 2-1/4”) will be higher than full-frame 35mm, which will be better than APS size, which will have an edge over 4/3, which is better than 1/2.3”, etc, etc.

Of course, as I said, pixel size is not the sole determinant of image quality. There are others:

  1. CCD sensors perform better than CMOS sensors.
  2. Sensor quality differs between sensor chip manufacturers.
  3. Sensor quality varies within the range of products from any one sensor manufacturer. Every product line has a high-end line and a low-end.
  4. Furthermore, any one maker of cameras e.g. Nikon may use sensor chips from different manufacturers between their camera models. So they might put a cheap sensor from one manufacturer in a cheap camera, but a pricey sensor from another manufacturer in their high-end camera.
  5. Newer sensor technology is surely better than older technology, because chip manufacturers are getting better every year, improving the optical and electrical characteristics of sensors. Thus the technology's generation matters.
  6. Optics can play a big role at high megapixels. Not all lenses are equally finely polished. Some high-MP cameras are being sold with lenses that are just barely sufficient to support the number of megapixels. Some cameras with over 12 megapixels are being paired with lenses that are not ground fine enough to support that many pixels.
  7. Lastly, whether sub-pixels (red, green and blue) are adjacent versus stacked is a big factor in image sharpness. (Stacked sub-pixels are used in Foveon sensors. Adjacent are used in Bayer sensors.)

Now that we’ve delved into the macro world of sensors, and how they impact image and photo quality, it is time to jump into the micro world of sensors and see how they are made. I’ve alluded to specifications such as pixel pitch in microns, but there is a lot more to discuss such as IR filters, sensor lenses, and many mechanical and electronic issues. That will be our next topic as we continue our journey through the science of photography. So, until next time, I won't say good-bye, I'll say "see you soon."


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The Science of Photography -- Part Eight

I haven’t used the term before, but a useful concept that collects all the “half or double” I’ve been expounding for several chapters as it relates to shutter speed, f/stop, and even sensor sensitivity in ISO values is EV or “Exposure Value.”

To quote from Wikipedia, “In photography, exposure value (EV) denotes all combinations of a camera's shutter speed and relative aperture that give the same exposure. In an attempt to simplify choosing among combinations of equivalent camera settings, the concept was developed by the German shutter manufacturer Friedrich Deckel in the 1950s. Exposure value also is used to indicate an interval on the photographic exposure scale, with 1 EV corresponding to a standard power-of-2 exposure step, commonly referred to as a stop.”

EV charts usually assumed an ASA or ISO value of 100, but EV can also be used to describe specific values of ISO settings on digital cameras. This was not as much of an issue with film, because you had to change film to change ISO. Now, with digital sensors, the sensitivity setting is yet another variable for the camera to set automatically, or for a knowledgeable user to adjust. My Nikon D7000 has ISO starting at 100 and adjustable by 1/3 EV values up to a top value unheard of with color film. Although the staggering large values above ISO 6400 are done with digital tricks, it can extend the sensitivity out to 25,600. You won’t even need a moon lit night with those high numbers, a few stars in the sky will make the dark as bright as day. Every advance in camera technology seems to move the ISO number upward and be less impacted by noise.

In the last installment of the "Science of Photography," I introduced the myriad of available digital light sensor sizes. What is really amazing to me is how many individual sensors, called pixels, they’ve crammed onto a small piece of silicon. So let’s dig into sensitivity and resolution. We will discuss this very physics based topic for both film and digital sensors and I’ll try to keep the water from getting too deep. But, we’ve just been wading the the shallow end of the pool. The topics to come are pretty deep and those who are not experienced swimmers in math, physics, and optics, may gulp down a few mouths-full of water. If it gets too deep, you can always glaze over and the look at the pictures.

Sadly, this medium of Facebook Notes does not allow for good pictures and illustrations, but I’ll do my best to create some word pictures. You can also do some searching on the Internet for good articles on these various topics. I’ll drop enough names to make some good Google search phrases.


Kodak

Before I wade into the pool, I have two brief asides. First is this news update from Kodak. The Kodak brand is an iconic name when it comes to associating it to photography and cameras. Back in the days before digital technology many amateur and professionals alike used their critically acclaimed 35mm film. Now it has been announced that the Kodak EasyShare range of cameras are to cease production as the company looks to further cut costs. It's the end of an era.

Last month the company filed for Chapter 11 bankruptcy protection in the US as it attempts to restructure and survive. But now the company has announced that it is leaving the camera business.

Kodak currently has over 1,000 digital imaging patents that could prove invaluable as it looks to secure its long term future. Not only am I very sad to hear of the end of Kodak cameras because of my experience with film, but Kodak was also a pioneer in the development of digital cameras. That is one reason it has such a large portfolio of patents.

Digital camera technology is directly related to and evolved from the same technology that recorded television images. In 1951, the first video tape recorder (VTR) captured live images from television cameras by converting the information into electrical impulses (digital signals) and saving the information onto magnetic tape. Bing Crosby laboratories (the research team funded by Crosby) created the first early VTR and by 1956, VTR technology was perfected (the VR1000 invented by the Ampex Corporation) and in common use by the television industry. Both television/video cameras and digital cameras use a CCD (Charged Coupled Device) to sense light, color, and intensity.

Texas Instruments patented a film-less electronic camera in 1972, the first to do so. In August, 1981, Sony released the Sony Mavica electronic still camera, the camera which was the first commercial electronic camera. Images were recorded onto a mini disc and then put into a video reader that was connected to a television monitor or color printer. However, the early Mavica cannot be considered a true digital camera even though it started the digital camera revolution. It was a video camera that took video freeze-frames.

Since the mid-1970s, Kodak has invented several solid-state image sensors that "converted light to digital pictures" for professional and home consumer use. In 1986, Kodak scientists invented the world's first megapixel sensor, capable of recording 1.4 million pixels that could produce a 5x7-inch digital photo-quality print. In 1987, Kodak released seven products for recording, storing, manipulating, transmitting and printing electronic still video images. In 1990, Kodak developed the Photo CD system and proposed "the first worldwide standard for defining color in the digital environment of computers and computer peripherals." In 1991, Kodak released the first professional digital camera system (DCS), aimed at photojournalists. It was a Nikon F-3 camera equipped by Kodak with a 1.3 megapixel sensor.

The first digital cameras for the consumer-level market that worked with a home computer via a serial cable were the Apple QuickTake 100 camera in 1994, the Kodak DC40 camera in 1995, followed by the Casio QV-11 with LCD monitor, late in 1995, and Sony's Cyber-Shot Digital Still Camera in 1996.

Kinko's and Microsoft both collaborated with Kodak to create digital image-making software workstations and kiosks which allowed customers to produce Photo CD Discs and photographs, and add digital images to documents. IBM collaborated with Kodak in making an internet-based network image exchange. Hewlett-Packard was the first company to make color inkjet printers that complemented the new digital camera images. All in support of the Kodak DC40.

The rest, as they like to say, is history! So now you know the rest of the story.


Crop Factor

In notes with family in Alaska, we’ve discussed using specific lenses on a wide variety of camera sensor sizes. In the case of the Lincolns, they have Canon cameras with sensors a variety of sizes from full frame (23.9mm x 35.5mm), to APC (16.7 x 25.1mm), to smaller 14.9mm x 22.3mm, and even the smaller 4/3” size. When you swap lenses around between cameras with different size sensors, I’ve already discussed the differences in normal view, wide angle, and telephoto. So how do you allow or compensate for these variations of lens performance on different cameras? One ratio has been designed to deal with the match of lens to sensor size and it is called “crop factor.”

"In digital photography, a crop factor is related to the ratio of the dimensions of a camera's imaging area compared to a reference format; most often, this term is applied to digital cameras, relative to 35 mm film format as a reference. The most commonly used definition of crop factor is the ratio of a 35 mm frame's diagonal (43.3 mm) to the diagonal of the image sensor in question; that is, CF=diag(35mm) / diag(sensor)." Crop Factor can be used to determine zoom lens equivalent focal lengths.

Rather than spending time describing crop factor, I suggest this Wikipedia article which I’ve quoted in the previous paragraph will explain it better than I can.  Check out:

http://en.wikipedia.org/wiki/Crop_factor

I think this explanation is about the best I’ve read and doesn’t require my poor attempt to explain. And that leaves me more time to talk about resolution. Let’s start with film.


Film Resolution

So, what is the resolution of film? With digital sensors, we often quote the total megapixels as if it was a pedigree. However, as we’ve stated several times, digital sensors come in different sizes. So a more meaningful value would be resolution per area called pixel density. That is, the total number of pixels in a given square area.

But I said I wanted to start with film. So what is the resolution of typical 35mm color film? There is no one answer, because film doesn't have to bother with pixels. With film, the image is continuous in all three dimensions: x, y, and z (intensity). With film, you get the same resolution at color transitions (green/magenta, for instance) as you get for light/dark transitions. With film, you have complete Red, Green, and Blue resolution at every point. (Color photography, either film or sensor, is done with three primary colors that are then combined to produce all the colors of the rainbow.)

Film's sharpness decreases gradually as the spatial frequency of fineness of detail increases. (Compare that to a whistle that is so high pitched, only a dog can hear it. Sharpness decreases on film for "high frequency" detail.) Film's response to detail gradually becomes less as the details get finer. This is best measured using a technique called the Modulation Transfer Function or MTF curve. MTF is the most widely used scientific method of describing lens performance

MTF applies to every imaging system, film or digital. Photographers see these charts in tech data sheets for film and for lenses. Film can resolve insanely fine details, but not with as much contrast as coarser features. This natural response is similar to our eyes, and another reason film looks so good. Digital, does not have this gradual transition and has a fine structure made up of discrete pixels. When you increase the size of film photos, the detail gradually disappears -- it just becomes blurry or fuzzy. With digital pictures, as you blowup the size of the picture, you start to see the fine structure. This is called “pixelation.”

I had an interesting thought that this is much like vacuum tube amplifiers vs. solid-state. Vacuum tubes have a much more gradual transition when they are over-driven into saturation when compared to transistors which shut off abruptly. That is one of the reasons that most musicians prefer vacuum tube amplifiers. It is a similar difference between film and digital sensors. Film makes the transition to fine detail a gradual function compared with pixelation.


Digital Film Scans

When you scan film, good scanners resolve right up to their DPI (dots or pixels per inch) rating. Film scans also have complete RGB color information and resolution at each pixel. Film scans resolve detail about as well as the original film, up to the resolution of the scanner. There is no response to details finer than the resolution of the scanner, even if it's on the film and visible in optical prints. When people compare film to digital, they are usually only comparing scans of film to digital.

With digital cameras, you get full contrast up to the very highest limit of the sensor's resolution. Finer details simply disappear, or become aliases. This is one way film and digital look so different. Film records fine and coarse details naturally, while digital (and video) tend to record medium details more strongly than film, but have no response to the extremely fine details which film can record.

Often the finest medium details to which the digital camera is sensitive are boosted in contrast. This is called sharpening, and is how we get digital images to fool the eye into thinking they're sharp.

Digital cameras never resolve their rated resolution. The only digital cameras that do were those with Foveon sensors, but then Sigma started lying, too. Let me explain:

The Foveon sensor is a CMOS image sensor for digital cameras, designed by Foveon, Inc. (now part of Sigma Corporation) and manufactured by National Semiconductor and Dongbu Electronics. It uses an array of photosites, each of which consists of three vertically stacked photodiodes, organized in a two-dimensional grid. Each of the three stacked photodiodes responds to different wavelengths of light, that is colors. This difference is due to that fact that different wavelengths of light penetrate silicon to different depths. The signals from the three photodiodes are then processed, resulting in data that provides the three additive primary colors, red, green, and blue. The key point is that each pixel location produces full color.

So the Foveon sensor produces the colors without the use of filters. Other, (non-Foveon) digital cameras use a black-and-white sensor on which red, green and blue dots have been painted. The painted dots act as color filters. That means it takes three distinct sensors to fully resolve the color of a pixel.

That means it takes more than one individual sensor to produce a complete color pixel, since only one-third of the sensor is painted with each color, firmware in the camera (or in raw conversion software) takes the pixels of each color, and interpolates (smoothes) values in-between the pixel locations of each color to create brightness value for each color at every other color's location.

Actually there are two green sensors for each red or blue. A Bayer array consists of alternating rows of red-green and green-blue filters. Thus the Bayer array contains twice as many green as red or blue sensors. Each primary color does not receive an equal fraction of the total area because the human eye is more sensitive to green light than both red and blue light.

Therefore, at each pixel location in a digital camera's image, we don't have full RGB data. We only get about half, which is why digital camera images at 100% won't look as good as good film scans at 100%, or lower resolution settings of your camera seen at 100%.

This is all called Bayer Interpolation. With this, most digital cameras really only resolve about half their rated megapixel rating. For instance, a 10MP camera really only sees about as well as a theoretically perfect 5MP digital camera, or 5MP film scan.

Foveon chips see at full resolution, but the makers of those cameras lie about the resolution to keep up with other cameras. Most Foveon-chipped cameras multiply the real resolution by three! What Sigma sells as 14MP cameras are really only 5MP. So, who yah gonna believe? There are lies, damn lies, and sales literature!!

So how many pixels does it take to describe all the detail we can get from film?

With all my positive talk about Kodak earlier -- and I was always a Kodak film user in my day -- Fuji Velvia film has been the choice of professional photographers since the 90's. Fuji Velvia 50 is rated to resolve 160 lines per millimeter. This is the finest level of detail it can resolve.

In order to convert the film resolution to digital terms, assume each line will require one light and one dark pixel, or two pixels. Think of it like a checkerboard with black and white squares. Thus it will take about 320 pixels per millimeter to represent what's on Velvia 50.

320 pixels x 320 pixels is 0.1MP per square millimeter.
35mm film is 24 x 36mm, or 864 square millimeters.

Therefore, to scan most of the detail on a 35mm photo, you'll need about 864 x 0.1, or 87 Megapixels. But wait: each film pixel represents true R, G and B data, not the softer Bayer interpolated data from digital camera sensors. A single-chip 87 MP digital camera still couldn't see details as fine as a piece of 35mm film.

Since the manufacturers count every sensor, even though it takes two to get a full color pixel, you'd need a digital camera of about 87 x 2 = 175 MP to see every last detail that makes onto film.

That's just 35mm film. Pros don't shoot 35mm, they usually shoot 2-1/4" or 4x5." At the same rates, 2-1/4" (56mm square) would be 313 MP, and 4x5" (95x120mm) would be 95 x 120 = 11,400 square millimeters = 1,140 MP, with no Bayer Interpolation. A digital camera with Bayer Interpolation would need to be rated at better than 2 gigapixels to see things that can be seen on a sheet of 4x5" film!

As we've seen, film can store far more detail than any digital capture system. The gotchas with any of these systems is that:

1.) It takes one heck of a lens to be able to resolve this well.
2.) It takes even more of a photographer to be able to get that much detail on the film, and
3.) If you want to scan the film and retain this detail, you need one quite a scanner (320 lpmm = 8,000 DPI).

As digital film scanners improved over time and increased resolution, we saw more details. You can argue that no digital scanner has ever equaled the resolution of film. Consumer 35mm scanners have topped out at about 5,400 DPI and we still saw more detail in our scans than we did at 4,800 DPI -- a value I've some times seen given for 35mm film. Obviously, it is not correct.

Film never stopped amazing us as we scanned it at higher and higher resolutions, and this is why.

5,400 DPI is equal to 212 pixels per mm, or 0.045MP/mm^2. Thus a 35mm slide, scanned on that 5400 scanner, yielded 39MP images, without Bayer Interpolation. Open these in PhotoShop, and 39x3 = 120 MB files, again, sharper than the Bayer-interpolated images from digital cameras.

By the way, even though I keep calling these sensors in digital cameras, digital sensors, they are actually analog sensors and the analog output is processed into a digital picture using the Bayer Interpolation implemented as a software algorithm.

And that is a good place to stop for the day. I covered a lot more and wrote many pages more than I expected. It is fun to get into the film and lens discussion and MTF. I'll explain that more, but -- if I'm not careful -- the next thing you know I'll be talking about Fourier Transforms and soon that will lead to Euler's Equation (what I consider the most beautiful equation of all time). I'll save that for next time.


http://mickey-cheatham.blogspot.com/2012/09/the-science-of-photography-part-nine.html

The Science of Photography -- Part Seven

In the last episode, we learned the three things that affect depth of field: f/stop, lens focal length, and distance to the subject. In a deeper examination of the impact of focal length, we learned that the size of the film or sensor determines the way the subject being photographed is displayed -- it’s size or field of view--and that this is often referred to based on a central lens size called a “normal lens.” Lenses with focal lengths less than "normal" are considered wide angle and lenses with focal lengths longer than the "normal" value are considered telephoto lenses.

The interesting thing is that the value of focal length that is considered “normal” depends on the sensor size. In the days of film photography, when 97% of cameras used 35mm film, this was not an issue. A 50mm lens was considered "normal."

But in this new age of digital cameras, most sensors are smaller than 35mm, and many are much, much smaller. This changes the lens focal length that is considered this median, normal value, and some old habits and assumptions are not correct. There are advantages to the smaller sensors because they allow for smaller and cheaper optics to work, but there are disadvantages too. As usual, at least in my opinion, knowledge is the key to using these new, smaller cameras and that is the business I’m in -- the knowledge business. So, lean back, grab a hot beverage, and enjoy this chapter of the Science of Photography as we learn more about the impact of different sensor sizes.


The important thing to understand is that, when you buy your camera or camera body, the size of lens that is considered “normal” may be different than you expect, and the ranges of lens focal lengths for wide angle, “normal” and telephoto views is based on the size of the sensor in the camera. I’ll start with a description of what determines a "normal" lens for a camera. Once you know what the normal lens is (and I’ll quit putting the term in quotes from now on), you'll know that any focal length shorter than that is wide angle, and the shorter it gets, the wider-angle it gets, and that anything longer than normal is telephoto, and the longer it gets, the more telephoto.

Figuring out the focal length that determines a normal lens is pretty easy. All you need to know is the size of your film or sensor. The normal lens focal length is generally considered to be equal to the diagonal of the image size.

Lens focal lengths even on small point and shoot cameras are often referred to in terms of their 35mm equivalents, so I am going to start with 35mm film/full frame digital sizes as a reference. In 35mm film cameras, the actual image size is 24mm x 36mm.

Film formats are rectangular or square, and square corners means ninety degrees, so to figure the diagonal, you use the formula for the hypotenuse of a right triangle. You remember: the square root of the sum of the squares of the other two sides. Sure, the Pythagorean Theorem, I remember it well!

It's easy. With 35mm film, add 24 squared (576) plus 36 squared (1,296) and you get 1,872. Take the square root of that number and you get 43.3. That is the size of the normal focal length for a 35mm camera. A lot of 35 mm cameras had a 50mm lens, slightly longer than the 43mm calculated as the size of the normal lens.

We will repeat this calculation for smaller sensors, and you may wish to calculate the normal lens focal length for your camera and sensor size. Do be careful if you do this with a simple calculator. If you enter the first number, and then press the x-squared key, that’s fine. If you then press the plus key and enter the second number and then press x-squared, you won’t get the second number squared, but you’ll get the first number squared plus the second number, that entire sum squared. I suggest you square each number individually and write down the values. Then add those squares and take the square root of the sum. You can also use parentheses on the fancy calculator or use calculator memory to save values. I just wanted to warn you about a common calculator mistake. If you’re not sure, you can even do the squares by hand. You may find the square root calculations a little hard to do manually, although it can be done and the method was taught, around sixth or seventh grade. But, now we have calculators. Thank God for calculators! I also link to several web sites which will help you find the length of the diagonal for your camera’s sensor.

So what is the significance of all this ancient cameras and more ancient mathematics -- whether from sixth grade or the much older greek method of determining the hypotenuse? Most 35mm film SLRs came with a 50mm lens as the normal lens, slightly longer than the 43mm calculated above. A 50mm lens was typically the standard lens installed on cameras in those days. A few compact film cameras came with 35mm, 40mm, or 45 mm lenses.

Anything shorter than 43mm would be a wide angle lens, anything longer telephoto (actually, 50mm is hardly telephoto, just sort of a long normal).

One of my early cameras was a Konica C35 rangefinder camera. It had a 35 mm lens, and was a good example of these smaller cameras with a slightly wide angle lens. It had a built-in exposure meter and shutter speeds from 1/30 to 1/650 of a second automatic tied to the exposure meter. You would set the aperture f/stop and the camera automatically set shutter speed for correct exposure. It had an f/2.8 lens and a dial to set the film speed. It would calculate exposure for film speeds from ASA 25 - 400. ASA was an early American predecessor of the current, international ISO value.

As I asked earlier, what is the significance of all this ancient math and normal lens focal length? Why would we care? It is because, in this day and age, most digital cameras have sensors smaller than the 24mm X 36mm area of 35mm film. In fact, that size is huge compared to most small cameras today. DSLRs have larger sensors, but even most DSLR cameras don’t have senors as big as the old 35 mm film. Only the top, professional, and expensive models have full sized sensors.

So assuming that 43mm or even 50mm is the dividing line between wide angle and telephoto is not correct. With smaller sized sensors, the normal lens size is smaller -- maybe a lot smaller.

Both of my  digital SLRs have APS size sensors, about 2/3 the size of 35mm film. APS stands for “Advanced Photo System,” a late attempt at a simple consumer film format for those for whom loading and rewinding 35mm was too complex. The typical tiny compact digital point and shoot camera has even smaller -- actually tiny sensors, and cell phone cameras have teeny-tiny sensors.

You can check the technical reference data in your cameras manual or on the web to see what size sensor is in your camera. Remember, a smaller format sensor or film is going to take a shorter lens to be normal, and shorter focal lengths have greater depth of field.

I’ll save you the calculations and list a few common camera’s sensor size and resultant normal focal length. What I haven’t mentioned so far is that, in the days of film, there were cameras with film size larger than 35mm such as the Hasselblad two and a quarter inch camera. This is true today too, with some expensive cameras having very large sensors such as the professional Hasselblad digital camera. I’ll list those too.

(Unfortunately, FB Notes does not have good table formatting, so you’ll just have to bear with this and make the best that you can of the following list.)

Camera                                Sensor Size                    Normal Lens

Speed Graphic Press             4” x 5”                                  162mm
Film Camera                        101.6mm x 127mm  

Hasselblad Film Camera       2 1/4 inch squared                 85mm
                                            60mm x 60mm  

Hasselblad Digital                36.8mm x 49.1mm                 61mm

35mm film                           24mm x 36mm                       43mm

Nikon D3                             23.9mm x 36.0mm                  43mm

Canon 5D                            23.9mm x 35.5mm                  43mm

Canon 60d                          16.7 x 25.1mm                        30mm

Nikon D7000                      15.6mm x 23.6mm                   28mm

Canon T2i                           14.9mm x 22.3mm                   27mm

Olympus PEN and                13.0mm x 17.3mm                   22mm
Panasonic Lumix                 4/3” Micro Sensor

Canon G12                          1/1.7”                                      9.5mm
                                           5.7mm x 7.6mm

Small Canon                        1/2.3”                                      7.7mm
                                           4.12mm x 6.16mm

iPhone                                 2.68mm x 3.58mm                 4.5mm    

Finally, I just read of an experimental sensor produced by Canon and billed as the world’s largest (and the most sensitive). It is 202mm x 205mm for a normal lens focal length of 288mm. I suspect that sensor will be put into an astronomical telescope or some sort of CIA satellite. Only the government could afford the cost of the lens needed to match that sensor!

If you would like to read more about sensor size, view a few more common camera sensors, and even see representations of these sensors -- drawings of just how big they actually are (although it does depend on the size of your computer screen) -- then check out this web site:

http://www.uscoles.com/sensorsandlenses.pdf

I also found this to be a good site for reference:

http://www.dpreview.com/learn/?/Glossary/Camera_System/sensor_sizes_01.htm

You can look up your personal camera on the internet and find the sensor size and calculate its normal lens depth of field and compare to the above table. Now for the application. Remember, the shorter the focal length, the greater the depth of field. Tiny cameras like those in cell phones have such short normal lenses, and you can assume these fixed lens cameras probably have normal focal length lenses, that they have a giant depth of field. As I’ve said before, that’s how they can get away with not having any focus adjustment. But, with those cameras, you are not going to be able to operate with a narrow depth of field and be able to have part of your picture be out of focus. That eliminates a lot of artistic effects.

Not only are these calculations good for determining what size lens is normal, but a lot of modern zoom lenses are specified with their “35mm camera equivalent focal lengths.” That can be confusing, especially if you don't notice the distinction between actual focal length and the equivalent lengths.

Here is a web site with a focal length comparison tool to allow you to make that kind of comparison:

http://tamron-usa.com/lenses/learning_center/tools/focal-length-comparison.php

For example, the Canon The EF-S 55-250mm f/4-5.6 IS, which -- as it says -- is a 55-250 mm lens intended for use with APS sensors. In the Canon technical description it states the 35mm camera equivalent zoom is 88-400 mm. So you old time photographers who considered a 400mm lens as pretty long glass, notice that this 250mm max zoom lens is equivalent when used with a small, APS sensor.

There is more to say. Now that we’re on the subject of sensors, what about the sensor resolution? You know, those megapixels you’re always hearing about. What about them? At this rate I may never get this series on the “Science of Photography” done.

OK, I’ll explain about sensor resolution and the science behind that modern wonder. I’ll have to write fast because this is changing all the time. So, wait until tomorrow to hear more about sensors. Their size and other goodies. Until then, TTFN.


http://mickey-cheatham.blogspot.com/2012/09/the-science-of-photography-part-eight.html

The Science of Photography -- Part Six


Now, to bring this all together, we know that the shutter speeds and f/stops both double and halve. Thus, we know that we can open up an f/stop (letting in twice the light) and move the shutter speed one step faster (cutting the time in half) and have the same amount of light on the film. It's like that bucket of water; run the water twice as fast for half the time and the bucket is still full.


We have covered in great depth the doubling/halving relationship and how it works with f/stops and shutter speeds to control exposure. You now understand that, for a given illumination on a subject and a given ISO, there are many combinations of shutter speeds and f/stops that give the same amount of light on the film or sensor. This is key point since the shutter speeds and f/stops you choose have implications in how your final photograph will look in ways other than just the amount of light on the film. For example, as you stop down the aperture, you get more depth of field.

If you don’t have a tripod, there are limits to how slow your shutter speed can be before your body movements blur the photo, so there are some constraints. But the point remains, all these combinations yield the same amount of light on the film and an identical picture in terms of brightness. What does vary is the ability of the camera to stop action and the depth of field, or how much is in focus in front of and behind the subject. That is the topic I want to discuss next -- depth of field.


Depth of Field

Depth of field is the amount of subject matter in front of and behind your focus plane that appears to be in sharp focus. When we say "that appears to be in focus" or "is acceptably sharp", understand that this is a continuum, it's not like objects in the depth of field range are razor sharp and then suddenly the sharpness abruptly becomes fuzzy. Things get gradually less sharp until they are perceived as being "out of focus". It is very much like a normal or Gaussian curve.

Basically, these three things affect depth of field:

1. The f/stop

The smaller the f/stop (the larger the number, that is, the smaller the diameter of the aperture), the more depth of field you get. At f/2 (small number, big aperture), you will have comparatively narrow depth of field, with little in focus on either side of your focus point. At f/16 (big number, small aperture), you will have comparatively more depth of field, with more subject matter in focus on either side of your focus point.

I say "comparatively" for a reason. As I’ve already discussed, from a brightness point of view, measuring the amount of light hitting the film or sensor, f/2 is f/2 regardless of the lens. This isn't the case with depth of field. The amount of depth of field at f/2 will also depend on ...


2. The focal length of the lens

The shorter your focal length, the more depth of field you will have. A 25mm lens will have more depth of field than a 50mm, and a 50mm will have more than a 100mm. With really short lenses, like 4 mm, you will have immense depth of field.

That is how simple cameras work. They have a small lens with a fixed focus, but the depth of field is such that everything from one foot to one mile is in focus. That is how the camera in the iPhone works. It has no focus adjustment, but it has a very small lens. With long lenses (telephoto), like a 400mm, you will have a very small depth of field. (Note that you usually have a relatively high f/stop on long lenses, so the depth of field limiting is not so severe, but it is there.)


3. The distance to the subject

The closer you are to your subject, the less depth of field there will be. The further away you are, the more depth of field you will have. Depth of field is actually a percentage of the distance around the focus point. So, at one foot it may be one inch, but at ten feet it is ten inches and at 100 feet it is 100 inches or a little over 8 feet.

Narrow depth of field can be obvious in some photos. Portrait photography is a pretty standard use of limited depth of field. Portraits are typically taken with the subject close to the camera and an f/stop of f/1.4 - 2. That way the subject is in sharp focus, while the background is out of focus yielding a "soft" effect and forcing the eye to go to the person. The point of a portrait is the person being photographed, and not the background. It is also possible to focus on a distant object, and have the foreground be softly out of focus. Very artistic shots can be composed using these techniques.

That second item, the focal length of your lens, has an interesting aspect to it. On one hand, it's pretty straightforward in that the depth of field of a 50mm lens at, say, f/8, is the same regardless of what camera the lens is on.

The wrinkle is that the 50mm lens can be wide angle, normal or telephoto depending on the camera body to which it is attached and format (size) of the film or sensor of that camera. In the days of 35mm film, a 50mm lens was considered "normal." Less than 50mm was called "wide angle" and greater than 50 mm was considered telephoto.

This sounds like some theoretical detail, not significant to we simple photographers, but in fact has some important implications in this digital age. This is because in the film days, just about everyone used 35mm film and lenses in the same focal length range. Now, with digital cameras, sensor sizes vary from tiny to full-frame 35mm sized and even beyond.


Sensor Size

With modern digital cameras, there is no standardization on sensor size, and each size comes with its own requirements for focal lengths and even lens design. In general, now that digital has taken over, sensors are smaller, the lenses are shorter, and the depth of field is greater. In fact, recent technological changes have led to even smaller sensors with yet higher resolution. If you want everything in focus all the time, this is great. If you'd like to be able to make some things out of focus ever once in a while, this can be a problem.

Why would a photographer want something not in focus? As I explained earlier, it is actually a great artistic effect, and you may not want everything in focus all the time. It's a way to force the observer to the important parts of the photo by making other parts out of focus. It can be part of the composition of the photograph. We're really moving from the science to the art of photography here.

Sadly, if all you have is one of those lovely little digital cameras or the camera in your cell phone, you will find it easy to get lots of depth of field and surprisingly difficult to get limited depth of field. This has to do with the relationship of film formats and sensor sizes to the focal lengths of lenses used. That is one reason to spend more for cameras which allow direct adjustment of exposure controls, larger sensors, and -- even -- removable lenses. If you do own a camera with interchangeable lenses, this will be a guide to which lenses you should have in your collection and for what reason.

This large depth of field of the simple pocket cameras can be annoying because limited depth of field, to make your subject stand out against the foreground and background, is a pleasing way to isolate and emphasize your subject.

In fact, a lot of filmmakers are quite interested in this fact as DSLRs are being used to do high-definition video for this very reason; they get to use longer lenses and get less depth of field and, in addition,  the ability to do real wide angle work without spending a fortune on wide angle lenses. This is called the "film look". A big part of this is the limited depth of field resulting from longer lenses and smaller sensors. Video photography is benefiting from this without resorting to expensive equipment.

In the next installment, I’ll go into this more. Remember, my goal is to explain everything there is to know about focus and exposure. So watch for the next installment and we’ll dig into sensor sizes and how they relate to focal length, lens classifications, lens selection, f/stops, and other esoterica. Plus, and you're going to really love this, we get to do more math. Not only are we going to square numbers, but we're going to take square roots. Why I can hardly wait for it.


http://mickey-cheatham.blogspot.com/2012/09/the-science-of-photography-part-seven.html

The Science of Photography -- Part Five

Now that we’ve conquered both shutter speed and f/stops, and are well versed in the idea of “double / halve” the light, we are ready to apply these concepts, along with film or sensor speed (ISO), to determine a correct exposure setting.

We will establish the meaning of the often spoken “stopped down” or less often spoken “stopped up,” and will learn to apply that concept to f/stop settings as well as shutter speed and film or sensor ISO values.

Finally we will discuss various concepts and ideas such as half stops and one-third stops. There’s more to be said about exposure control, and in this installment we will say it.


Exposure Control

Suppose you have determined that the correct exposure for the current film or sensor setting (ISO) is 1/125 at f/8. You may have determined that with a hand held light meter, or -- in this day and age -- your camera’s automatic exposure control has indicated these values.

(Now the whole point of all this discussion is to not set your camera on full automatic, but rather to have some control of the settings. This may be done by setting the camera in “Aperture Priority” mode, where you set the f/stop and the camera automatically sets the shutter speed; or you may use “Shutter Priority” mode which is the opposite. There is even a “Manual” mode where you set both. But, typically, the camera automatically sets the other exposure parameters or values to match the one you set manually. In simple point and shoot cameras, these are often called “scenes” which automatically set shutter speed or aperture to extremes.)

(But the point of this series of articles is for you to understand the implications of shutter speed and f/stop, even if you aren’t controlling it manually. So let’s assume you are.)

As I was saying, suppose you determine that the correct exposure setting is 1/125 shutter speed and f/8 aperture. BUT ... there’s more of that “but” -- you want a faster shutter speed. You want to capture the beating of a bird’s wing, for example.

The answer is simple. If you decrease the shutter speed by one stop, to 1/250, then you just open up the aperture by one stop, to f/5.6. (Remember, the smaller f/stop number means more light. You need a bigger “stream” of light to compensate for holding the hose over the bucket for less time -- bucket analogy.)

Or, suppose you’re taking a picture of a moving brook with water splashing over the rocks and you want a very artistic view where the running water is blurred into a steady white froth and only the actual still items in the scene are crisp focus.

Answer: slow the shutter down by five stops to 1/4 a second, and stop the lens down by five stops to f/45. Oh, oh, you say. Your lens only goes to f/22! And you want to set the shutter speed even lower!!  Well, there’s a fix for that too, but let’s hold off on that for the moment.

At least the first example showed, you can adjust either the aperture or the shutter speed up or down as long as you adjust the other control the same amount, in the opposite “direction,” to compensate. That was the whole point of all the half light / double light description of both controls. Here is a chart that you could use in the above example. This chart actually came right off my old hand held light meter.  I would dial in the film ISO on a sort of circular slide rule, and then read off various settings based on the value in the light meter. The slide rule calculator then gave me the combination of shutter speed and f/stop to properly expose the film under those measured light conditions.

  Shutter Speed    1/4     1/8     1/15    1/30    1/60    1/125
  F/Stop               f/45    f/32    f/22     f/16     f/11     f/8

  Shutter Speed    1/125    1/250    1/500    1/1000    1/2000    1/4000
  F/Stop               f/8         f/5.6      f/4       f/2.8        f/2        f/1.4

Basically, you can match almost any shutter speed with an appropriate f/stop to go with this particular light condition and obtain a proper exposure, at least within the limits of the values of aperture available on your lens.

I think you can imagine reasons to adjust shutter speed. You might want a very fast shutter speed if your taking a picture of something in motion which you’re trying to freeze. I remember taking pictures of cars on the drag strip as they passed me back in high school. Unfortunately, I didn’t set the shutter speed high enough and they are all blurred.

Or, maybe you do want a blurry effect like in the artistic photo of a small stream I mentioned earlier or maybe you want the cars to be blurred to represent the speed in contrast with the still background.

Those would all be reasons to adjust the shutter speed either up or down to obtain the effect you wish in the photograph. You then adjust the f/stop to get the exposure correct with that particular shutter speed.

But there are also reasons to adjust the f/stop up or down and then adjust the shutter speed to compensate. You see, the f/stop determines a focus characteristic called “depth of field.” If you want a scene containing near objects and far objects to all be in focus, you use a high f/stop number (stopped down lens), and if you want the opposite, only items close to the lens to be in focus and the background to be blurry -- for example in a portrait of a person, then use a wide aperture setting such as f/1.4 or f/1.8.

I’ll explain this depth of field issue in more detail in a later installment of this series, but -- for now -- realize that you may wish to adjust the f/stop to a particular value and then adjust the shutter speed to set the exposure. They were designed to work together and that is the whole point of all this half / double stuff.

Speaking of half or double, what if you want a finer adjustment and don’t want to reduce the light by as much as half or double? Well, in the old days, due to limitations of mechanical devices, shutter speeds were typically fixed at the values I’ve noted so far. But it was relatively easy for the camera manufacturer to have the f/stops be adjusted by incremental amounts. Usually these values were half of the regular amount, which would be half of a half equal to one-quarter reduction or, on the larger aperture, instead of double (200%) the light, you want to get 150% more light. These were called “half stops,” not to be confused with the fact that the standard f/stops cut light in half. This meant half of the standard stop.

Even finer control was to be had with 1/3 stops. And some cameras even had continuous adjustment with the f/stops just marked on the lens.

In modern digital cameras you can usually adjust the aperture by half or third stops and the notation is usually something like -1/2, -1/3, +1/3, and +1/2. Although I suspect that modern digital cameras can also adjust the shutter speed continuously, I don’t think that is common. Besides, as we’ve learned, either the shutter speed or the aperture can equally adjust the final exposure amount.

(It is also possible to set the overall exposure to higher or lower values when using automatic exposure control. I won’t get into that here, but that is also shown as +1 or -1 or even +1/3 or - 1/2. With automatic exposure control this would mean one stop or a partial stop brighter or darker, regardless of if it uses f/stop or shutter speed to make the adjustment. It’s all automatic in the little computer in the camera.)

Now let’s finalize our nomenclature. When we say “stop down” we mean reduce the amount of light. When you stop down a lens, you are going to a larger number/smaller aperture and therefore less light.

You can do that by changing shutter speed to a faster setting or closing down the aperture ... or even by adjusting the ISO value. Typically, photographers will say “stop down” to mean “one stop down.” You could reduce shutter speed from 1/125 to 1/250. Or you could change f/stop from f/8 to f/11 -- remember: higher f/stop number equals less light. Or you could even change ISO from 200 to 100. That is one stop down in film speed.


Film Speed

About the only thing left to discuss is the ISO numbers. With film, you had little choice but to change the film in the camera to change ISO. You could get film developed in a special way that made it higher ISO, but the typical way to change film speed was to load the appropriate ISO film.

Film came in a variety of ISO values such as 100, 200, 400 and 800. There was also slower film in ISO 50 and 25 and even 16. Just from these numbers, you may have guessed that ISO values are just like shutter speeds. If you double the ISO number, the film is twice as sensitive. (A very popular Kodak film was ISO 64, so the “double/half” relationship wasn’t always true!)

So, in our earlier 1/125 at f/8 problem, let's assume we want to slow the shutter speed down for an effect. We want to change the shutter open time to one-half second. That is six stops up from 1/125. If we assume that was with ISO 400 film, we can change film (or sensor ISO) down four stops to ISO 25 (400 -> 200 -> 100 -> 50 -> 25) and stop down (increase) the f/stop an additional of two stops to compensate: f/16.

We increased the light by six stops with shutter speed, decreased the effect of the light by four stops with ISO, and added two stops of light reduction by closing down the aperture to f/16. That would be 6 - 4 - 2 = 0 change in exposure! With digital cameras which have adjustable ISO, this is common. (Just be careful turning the ISO up over 1,000 or 2,000 because the picture can become noisy, displaying colored confetti in a grainy effect.)

Now we have three parameters to control exposure, while one parameter, shutter speed also controls how moving objects are photographed, and the other parameter, f/stop, controls depth of field. We can “tune in” almost any photograph result we wish.

Now get out there, set those cameras to manual mode, and start adjusting. Artistic photographs have blur and movement and crystal clear focus. All are under the artist’s control.

We’re not done yet. I actually have more to say about f/stop and a lot to say about depth of field. But this is all for now. See you next time in installment six of “The Science of Photography.”


http://mickey-cheatham.blogspot.com/2012/09/the-science-of-photography-part-six.html

The Science of Photography -- Part Four

As discussed in earlier installments of the “Science of Photography,” you set exposure using a combination of shutter speed and f/stop to obtain the correct amount of light on the camera’s film or sensor. The shutter speed controls how long the film or sensor is exposed to the light coming in through the lens. The f/stop controls how much light comes in through the lens by varying the area of the aperture. For a given film or sensitivity indicated by the ISO number and the amount of light on the subject being photographed, there is a single correct amount of light for proper exposure. This amount of light can be obtained with different combinations of shutter speeds and f/stops.

Although the f/stop is a key control in photography, it is often a mysterious value, poorly understood by many photographers. Perhaps, in this age of fully automatic cameras, this is not a problem. But, as the saying goes, it is a poor workman who blames their tools. In this installment we continue to educate users about the mystery and wonder of the f/stop.

As I described in the last installment, the beauty of the f/stop is it is a consistent measure of the amount of light, independent to the specifics of lens such as focal length. So that means that f/8 is the same amount of illumination on the film or sensor independent of the lens’ focal length.

As I also mentioned previously, that was how handheld light meters were able to indicate settings  independent of the lens used on the camera. No mater what size of film or sensor (we will talk about how sensor or film size effects lens parameters later) or what lens is being used, a 1/125 at f/8 is the correct settings for proper exposure. That will work on a wide-angle lens, a standard lens, or even a 300mm telephoto called a “long lens.”

Lenses are described by their maximum aperture. (Remember, that is the largest aperture, indicated by the lowest f/stop value.) If you look in a catalog, you might find a 50mm lens with a measure of f/1.4 or f/2.0 or even f/3.5. You will immediately note that the smaller the f/stop number, typically the more expensive the lens. That is because the lower the f/stop value, basically the bigger the lens glass -- that is the diameter of the overall lens. The bigger or wider lens lets in more light, and that is reflected (no pun intended) by the lower f/stop number.

These larger and more expensive lenses are often called “fast lenses.” That implies that, under a given set of light conditions, the camera can use a faster shutter speed by setting the aperture to the widest value. That can be an advantage when photographing subjects in motion under low light conditions.

Given that fact, why doesn’t everyone use the fastest lens they can get? Well, first of all, as I said, the faster the lens the more it will typically cost. In addition, the larger diameter aperture means larger glass which adds weight. With larger and heavier lenses, you have to use heavier materials in the barrel supporting the lens. All in all, this increases weight.

Also, the larger the lens, the more perfectly it has to be manufactured to prevent visual imperfections. In fact, many experienced photographers will always stop down the lens at least one f/stop because the outermost edges of the lens are likely to have some distortion. By stopping down, you use more of the center of the lens.

I’ve actually found cheaper lenses that had less distortion than a faster (and more expensive) lens. In other words, if you don’t need the very low f/stop for your photography, you may be carrying around a lens heavier than you need, that cost more than a smaller lens, and -- saddest of all -- the smaller lens may actually perform better at f/8 or f/16.

Issues of size and weight are even more extreme with the so-called long lenses. For example, a particular Nikon 300mm lens, even though it is only f/4.5, weighs over two pounds. Compare that to another Nikon 300mm lens that is f/2.8. It weighs over five pounds. And Nikon’s 300mm, f/2 lens? It is over fifteen pounds. How would you like to lug that around? By the way, that f/2 lens costs over $20,000!

Most modern camera buffs use zoom lenses. Those are lenses that have adjustable focal length. These can be very useful lenses, adjusting to various focal lengths to match the shooting requirements. Modern zoom lenses are typically fairly light, but a check on the available f/stops shows they are not fast lenses.

In addition, you will notice that the f/stop values vary as you operate over the range of zoom. For example, a popular Nikon zoom lens varies the focal length from 28mm to 300mm, covering everything from wide angle to telephoto. However, the aperture on maximum changes from f/3.5 - 5.6 as you zoom out. Recall the f/stop is a ratio of the aperture diameter to the focal length, so this is to be expected.

The more expensive professional zoom lenses will have a constant f/stop across their zoom range, but those designs require additional weight and cost. Everything in engineering is a trade-off.

The weight difference is even noticeable on shorter lenses. Compare the Nikon 50 mm, f/1.4 lens with the cheaper f/1.8, and there is a noticeable difference in weight which can start to wear on you if you are shooting for an extended period of time. By the way, it is possible to find lenses with the aperture so wide they are f/1.0, but those are very specially designed lenses to deal with the issues of such a large lens and you will pay accordingly. The lowest f/stop I’ve ever seen was a Canon 50mm lens with an f/0.95. But, again, you will really pay in both dollars and weight for such a super fast lens.

In the days of film photography, photographers sometimes had to pay that cost to get the very best low light performance. Most 35mm film had ISO values of 100, 200, or -- at the most -- 400. There was super fast film with an ISO of 1000, but that was pretty much the limit unless you used very exotic film. So, in the days of film, very fast lenses were useful for low light conditions, especially with subjects that were moving so the shutter speed had to be 1/60 or higher to prevent blurring.

Compare the ISO values in film to the ISO values available in today’s digital cameras. Rather than souping up the film chemicals to be especially sensitive to light, digital cameras just amplify the sensor output. By increasing the gain of the amplifier, you effectively increase the ISO.  Modern, high end digital cameras can have extremely high ISO values.

My newest Nikon digital camera can have the ISO adjusted up to 6400, and special ISO modes go to 12,800 and 25,600. This camera has a 1/8000 second maximum shutter speed to match up with these superfast ISO settings. With the sensor so sensitive to light, you can still use fast shutter speeds, even with a high f/stop number.

There are problems with fast film or sensors. With film, the faster chemical formulas which responded to lower levels of light had a tendency to be “grainy.” This grain effect was caused by the individual elements of light sensitive chemicals making up the film. The faster the film, the greater the graininess. As I said, in engineering, there is always a trade-off.

In an interesting example of “duality,” a phenomenon where two similar physical methods demonstrate matching characteristics, digital sensors will also display graininess when the amplifier gain is turn up to increase ISO. In the case of digital sensors, the grain comes from amplifier noise at high gain settings. This is similar to the hiss you hear in an audio amplifier if you turn the volume control (gain) way up.

So, there is a penalty for using high ISO settings with a digital camera, but you can often turn up the gain and thereby the ISO to well over 1,000 without a lot of noise being added.

So, modern cameras with their very high sensitivity sensors can turn a slow lens into a fast lens. In fact, given this power to shoot in low light conditions, even with a slow lens, one must ask, “Why even bother with a fast lens?” They cost more. They weigh more. They are more likely to have optical problems than a slower lens. So what is an f/1.4 lens really good for? Why would you want one?

Those are good questions. And they are questions I’ll answer in the next installments of “The Science of Photography” as we start a discussion of “depth of field.” There are still other details to describe too, including “less than full f/stop - stops” and more on shutter speed combined with f/stop. Still a lot of science to cover in this art of photography. So, until the next episode, keep your powder dry and your camera dry too.


http://mickey-cheatham.blogspot.com/2012/09/the-science-of-photography-part-five.html

The Science of Photography -- Part Three

In my second installment of “The Science of Photography” I introduced the water bucket analogy and described in detail the shutter speeds available in modern cameras. The key to the explanation was that each shutter speed is either twice as fast or half as fast as the predecessor or successor value. That is the key point. This doubling or halving with each click of the shutter speed control will be combined with a similar double or halving of the light admitted by the lens with each click of the f/stop control.

In this article we will dig deep into the mystery of the f/stop. What it is, how it is calculated, and probably more math than you’ve experienced in the last week. There is a lot to say about f/stops. As authors like to say, the plot thickens.

Ultimately we will lean how f/stop is used in conjunction with the shutter speed control to adjust the total light that is admitted to the film or sensor. With proper adjustment of the variables, the amount of light will be just enough to “fill the bucket” and provide a correct exposure. But first, let me introduce you to, the value you’ve known for all these years, the f/stop.


F/Stops


An f/stop is a ratio. It is the ratio between the diameter of the aperture in the lens and the focal length of the lens. Therefore, f/stop is a characteristic of a given lens. Since most (good) lenses are made in either Japan or somewhere in Europe, the focal length is generally measured in millimeters, so that is the measurement I’ll use.

A very common lens has a focal length of 50 mm. Assuming a 50mm lens, then f/2 indicates that the diameter of the aperture is 25mm. That is, the ratio is 50/25 = 2 or f/stop = 2. So that seems pretty simple, although how it is useful for calculating the correct exposure may not be so clear yet.

Very simple lenses in very inexpensive cameras and in most cameras in cell phones are fixed aperture. That is, the aperture is not adjustable. But better cameras, that is more expensive cameras, have adjustable aperture.  The way it is made adjustable is by incorporating a set of between five and fifteen blades that can be adjusted inward and outward. The hole in the middle of the set of blades is roughly circular. We will use that fact in a few paragraphs, along with the formula for the area of a circle -- you know, the one with π, to calculate area. So stand by for some calculations.

But first, let’s look at some actual f/stop values:

1.4    2.0    2.8    4    5.6    8    11    16    22

This is the standard sequence of f/stops from f/1.4 to f/22. To begin with, you must realize that the f/1.4 setting lets in the most light while the f/22 setting lets in the least. The f/1.4 setting is when the aperture blades are retracted to their fullest extent and the f/22 is when the aperture blades are closed down to minimize the area the most. We say that the lens is “stopped down.”

Since the f/stop is part of a ratio or fraction, and it is really the denominator or bottom of the fraction, then, as the f/stop number gets larger, the ratio or fraction gets smaller. Compare 1/2 to 1/4. The larger four in the denominator makes the fraction smaller. That is why the larger the f/stop, the smaller the diameter of the aperture and the less light that comes in. Therefore, f/22 admits the least light into the lens.

Also, even though the sequence of numbers may seem arbitrary, each of these f/stops has precisely the same halving/doubling relationship as the shutter speed sequence. And therein lies the “magic.”

We can derive these numbers if we perform a little geometric mathematics. The aperture blades create a “hole” shaped as a polygon For example, with eight blades you get an octagon (looks like a stop sign). With a fifteen blade aperture, you get a pentadecagon, also called a pentakaidecon -- ain’t math fun!

However, it is OK to treat the aperture opening as a simple circle. Therefore the area of the opening is equal to π times the radius squared. That is, take the radius in millimeters, multiply it by itself, and then multiply that by approximately 3.1416. (Those wishing more accuracy can use 3.14159265 or even a longer approximation. Best would be to just press the π key on the calculator.)

Recall that our 50mm lens stopped down to f/2.0 meant that the aperture had a diameter of 25 mm. But, since we are interested in the amount of light admitted, we must calculate the area. If the diameter is 25mm, then the radius is half that for 12.5mm. Square the radius and we get 156.25. Multiply the radius squared by π gives 156.25 X 3.1416 =  490.9 square mm.

So the area of the 50mm lens aperture when stopped down to f/2.0 is about 500 mm squared.

Look at my list of f/stops above and you’ll see the f/stop to the right of 2.0 is 2.8. Let’s do some calculating on that value.

Because the f/stop is a ratio of the focal length to diameter, our 50mm lens at f/2.8 would have an aperture  diameter of 50/2.8 = 17.86mm. Remember, we have to divide that by 2 to get the radius of 8.93mm, so the area of the circle would be π X 8.93 squared, or 250.5 square mm. Rounding off a bit, that's about 250 sq. mm at f/2.8 and 500 sq. mm at f/2, a double/half relationship.

So the odd sequence of numbers isn’t so odd after all if you do all the converting from diameter to radius and squaring that number and then multiplying by three something. No wonder f/stops are so confusing.

But, on the other hand, they are simplicity indeed. Each larger number step to the right means half the light and each small number step to the left means twice the light up to the limit of the lens itself.

Now you may ask yourself, “why don’t they just call it the area of the aperture instead of these flakey f/stop numbers? Well, as confusing as f/stop numbers may be, think about using the diameter. “I took this picture with my 50 mm lens at 1/250th of a second and an aperture of 63 square millimeters.” Wait, you say. “That isn’t so bad. I like that better then f/5.6.” But, and here is the great beauty of f/stops, what if it was not a 50mm lens, but a 70mm lens. Then the actual area would be different -- BUT THE F/STOP WOULD BE THE SAME!

You see, all this f/stop business came from an era before cameras had built in light meters. In the old days -- also known as “when I was young” or “the time of the dinosaurs" -- we used hand held light meters and they would calculate shutter and f/stop settings independent of the focal length of the lens in the camera.

Knowing only the area of the aperture requires also knowing the length of the lens to understand the amount of light coming through the lens. The f/stop figure incorporates both of these in one useful, if initially confusing measure, and the lens length is immaterial. The f/stop is basically a shorthand notation for this important characteristic. When you set a lens to f/8, you mean for the focal length of this lens, open the aperture of the lens to a diameter that results in a circle that has a diameter that is one-eighth the value of the focal length. Fortunately for us, the lens makers figure out all these things and just mark the f/stops on the lens. So all those weird numbers are really for our benefit.

There is so much more to say about f/stop, but I’ll stop for now. In my next installment I’ll continue the thrilling story of the f/stop ... yes gentle readers, there is so much more story to tell. Ultimately, I’ll explain how to combine f/stop and shutter speed and control both the exposure and the effect you wish to capture. But you will have to wait for the next installment or two to reach that climax.


http://mickey-cheatham.blogspot.com/2012/09/the-science-of-photography-part-four.html