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#1
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The f/ratio myth and camera size
There are often questions about smaller versus larger pixels
and the corresponding camera size. Many of us would like smaller cameras that did just as good a job as larger ones. Is that possible? No, at least in terms of signal-to-noise that can be recorded. Here is why. There is a common idea in photography that exposure doesn't change between different size cameras when at the same f/ratio. For example, the sunny f/16 rule says a good exposure for a daylight scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100 second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16, a 35mm camera at f/16, an APS-C digital camera at f/16, down to the smallest point and shoot camera at f/16 (assuming the small camera goes to f/16). This leads people to think cameras scale easily and still give the same image. But there is a fallacy in this idea, and that is spatial resolution on the subject. The smaller camera, even at the same f/ratio, has a smaller lens which collects a smaller number of photons per unit time. The smaller camera gets the same exposure time because the UNIT AREA in the focal plane represents a larger angular size on the subject. The rate of arrival of photons in the focal plane of a lens per unit area per unit time is proportional to the square of the f-ratio. Corollary: if you keep f/ratio constant, and change focal length then the photons per unit area in the focal plane is constant but spatial resolution changes. So how does this apply to making smaller cameras? The problem is that if you scale a camera down, say 2x, the aperture drops by 2x, the focal length drops by 2x (to give the same field of view), the sensor size drops by 2x, and the pixel size drops by 2x (to give the same spatial resolution on the subject). It should be obvious by this point that per unit time the aperture has collected only 1/4 the number of photons. Also, the smaller pixels each collect 1/4 less photons since their area is divided by 4 to keep spatial resolution constant. Another way to look at the problem is aperture collects light, the focal length spreads out the light, and the pixels are buckets that collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE (ignoring transmission losses of the optics). Back to the camera example: scale a camera down by 2x keeping f/ratio and spatial resolution constant. You lose 4x the photons entering the lens with the smaller camera, and since you you must use 2x smaller pixels, the area is 4x less, so you LOSE ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a given resolution on the subject goes as the 4th power of the aperture (and camera size)! Decreasing your camera by 2x means 16x less photons per pixel if you want to maintain field of view and megapixel count! This is just what we observe with small cameras: their smaller sensors have smaller full well capacities, that get filled for a given exposure time with a smaller number of photons. That in turn means higher noise because there are fewer photons. Check out this web page for more info on this subject: http://home.earthlink.net/~stanleymm/f_ratio_myth.htm Roger Clark Photos, other digital info at: http://www.clarkvision.com |
#2
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The f/ratio myth and camera size
Higher noise under what conditions? If the shot has a sufficient
illumination level and the ISO setting on the camera is low enough, you should see no more noise from most small pixel cameras than from a large pixel camera. However, this only applies to scenes with relatively small illumination "spreads." If there are deep shadows (essentially, underexposed areas) then they will demonstrate noise to some extent. The question is, what pixel size is needed to keep noise relatively unnoticeable in shots with wide illumination ranges? My guess is that no current camera can produce a completely noise free image when all areas are taken into account, because none of them have the pixel well capacity and dynamic range to handle scenes with wide-ranging illumination levels. This is especially true when people insist on underexposing areas in order to "control" highlights in other areas. When they manipulate the curves of the image to bring out detail in the underexposed areas, those areas display noise, lack of contrast, depressed colour values and restricted tonal ranges. -Rich |
#3
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The f/ratio myth and camera size
Rich wrote:
Higher noise under what conditions? All conditions comparable between large and small cameras. If you have X photons with big camera A for a given f/stop and exposure time (e.g. 1/400 second at f/8), then on a small camera B for the same exposure and f/stop, you get less photons per pixel. Signal to noise ratio is the square root of the number of photons collected. The smaller camera collects less photons so has worse signal to noise. You might expose longer but smaller pixels have less capacity to store electrons (converted photons) so the smaller camera simply can never make up the difference. If the shot has a sufficient illumination level and the ISO setting on the camera is low enough, you should see no more noise from most small pixel cameras than from a large pixel camera. No. See above. However, this only applies to scenes with relatively small illumination "spreads." If there are deep shadows (essentially, underexposed areas) then they will demonstrate noise to some extent. It has nothing to do with illumination spread. Because less photons are collected by the small camera, the dynamic range is less too. The question is, what pixel size is needed to keep noise relatively unnoticeable in shots with wide illumination ranges? That is a subjective question with a variable answer, depending on the scene dynamic range and what is acceptable to the user. The fact is that we have many many wonderful photographs from film which has lower signal to noise than many point and shoot digital cameras, and on slide film with very narrow dynamic range. So P&S can still take great photos and in the hands of good photographers, many great images can be obtained. But a larger camera can generally do better, just like 35mm versus 4x5 film. My guess is that no current camera can produce a completely noise free image when all areas are taken into account, because none of them have the pixel well capacity and dynamic range to handle scenes with wide-ranging illumination levels. To get noise free, you need infinite photons, which is not possible. But tens of thousands of photons per pixel makes very high signal to noise images. The sweet spot in my opinion, are cameras with 6 to 9 micron pixels. There is no reason a small P&S camera could not have 8 micron size pixels with a pixel count over 8 million. Roger |
#4
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The f/ratio myth and camera size
Roger N. Clark (change username to rnclark) wrote:
There are often questions about smaller versus larger pixels and the corresponding camera size. Many of us would like smaller cameras that did just as good a job as larger ones. Is that possible? No, at least in terms of signal-to-noise that can be recorded. Here is why. There is a common idea in photography that exposure doesn't change between different size cameras when at the same f/ratio. For example, the sunny f/16 rule says a good exposure for a daylight scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100 second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16, a 35mm camera at f/16, an APS-C digital camera at f/16, down to the smallest point and shoot camera at f/16 (assuming the small camera goes to f/16). This leads people to think cameras scale easily and still give the same image. But there is a fallacy in this idea, and that is spatial resolution on the subject. The smaller camera, even at the same f/ratio, has a smaller lens which collects a smaller number of photons per unit time. The smaller camera gets the same exposure time because the UNIT AREA in the focal plane represents a larger angular size on the subject. The rate of arrival of photons in the focal plane of a lens per unit area per unit time is proportional to the square of the f-ratio. Corollary: if you keep f/ratio constant, and change focal length then the photons per unit area in the focal plane is constant but spatial resolution changes. So how does this apply to making smaller cameras? The problem is that if you scale a camera down, say 2x, the aperture drops by 2x, the focal length drops by 2x (to give the same field of view), the sensor size drops by 2x, and the pixel size drops by 2x (to give the same spatial resolution on the subject). It should be obvious by this point that per unit time the aperture has collected only 1/4 the number of photons. Also, the smaller pixels each collect 1/4 less photons since their area is divided by 4 to keep spatial resolution constant. Another way to look at the problem is aperture collects light, the focal length spreads out the light, and the pixels are buckets that collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE (ignoring transmission losses of the optics). Back to the camera example: scale a camera down by 2x keeping f/ratio and spatial resolution constant. You lose 4x the photons entering the lens with the smaller camera, and since you you must use 2x smaller pixels, the area is 4x less, so you LOSE ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a given resolution on the subject goes as the 4th power of the aperture (and camera size)! Decreasing your camera by 2x means 16x less photons per pixel if you want to maintain field of view and megapixel count! I believe you are off on this one. For the same f/number the photon flux at the sensor is the same. Take your case of scaling down a camera by a factor of two, the lens collects 1/4 the photons but it also spreads these photons out over 1/4the area that the larger camera does. The number of photons per sensor is therefor scales as the area of the sensor. So I believe you are looking at a 2nd power decrease not 4th. Scott |
#5
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The f/ratio myth and camera size
Scott W wrote:
Roger N. Clark (change username to rnclark) wrote: There are often questions about smaller versus larger pixels and the corresponding camera size. Many of us would like smaller cameras that did just as good a job as larger ones. Is that possible? No, at least in terms of signal-to-noise that can be recorded. Here is why. There is a common idea in photography that exposure doesn't change between different size cameras when at the same f/ratio. For example, the sunny f/16 rule says a good exposure for a daylight scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100 second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16, a 35mm camera at f/16, an APS-C digital camera at f/16, down to the smallest point and shoot camera at f/16 (assuming the small camera goes to f/16). This leads people to think cameras scale easily and still give the same image. But there is a fallacy in this idea, and that is spatial resolution on the subject. The smaller camera, even at the same f/ratio, has a smaller lens which collects a smaller number of photons per unit time. The smaller camera gets the same exposure time because the UNIT AREA in the focal plane represents a larger angular size on the subject. The rate of arrival of photons in the focal plane of a lens per unit area per unit time is proportional to the square of the f-ratio. Corollary: if you keep f/ratio constant, and change focal length then the photons per unit area in the focal plane is constant but spatial resolution changes. So how does this apply to making smaller cameras? The problem is that if you scale a camera down, say 2x, the aperture drops by 2x, the focal length drops by 2x (to give the same field of view), the sensor size drops by 2x, and the pixel size drops by 2x (to give the same spatial resolution on the subject). It should be obvious by this point that per unit time the aperture has collected only 1/4 the number of photons. Also, the smaller pixels each collect 1/4 less photons since their area is divided by 4 to keep spatial resolution constant. Another way to look at the problem is aperture collects light, the focal length spreads out the light, and the pixels are buckets that collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE (ignoring transmission losses of the optics). Back to the camera example: scale a camera down by 2x keeping f/ratio and spatial resolution constant. You lose 4x the photons entering the lens with the smaller camera, and since you you must use 2x smaller pixels, the area is 4x less, so you LOSE ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a given resolution on the subject goes as the 4th power of the aperture (and camera size)! Decreasing your camera by 2x means 16x less photons per pixel if you want to maintain field of view and megapixel count! I believe you are off on this one. For the same f/number the photon flux at the sensor is the same. Take your case of scaling down a camera by a factor of two, the lens collects 1/4 the photons but it also spreads these photons out over 1/4the area that the larger camera does. The number of photons per sensor is therefor scales as the area of the sensor. So I believe you are looking at a 2nd power decrease not 4th. Scott Scott, You are correct. I forgot to include that for the smaller lens at half the focal length, the area on the subject doubles, canceling one of the squared terms. So, yes, I agree that the relation scales as the square not as the 4th power. So halving the camera size means pixels get 1/4 the photons. A good example is the Canon 20D with 6.4 micron pixels and a maximum signal at ISO 100 of 50,000 electrons, compared to the Canon S60 with 2.8 micron pixels with a maximum signal of about 11,000 electrons at ISO 100. The pixel size is 6.4^2 / 2.8^2 = 5.2x scaling, similar to the 50000/11000 = 4.5 scaling of maximum recorded signal. Then, for photon noise limited systems, signal-to-noise ratio scales as the square root of the camera size. Roger |
#7
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The f/ratio myth and camera size
Roger N. Clark (change username to rnclark) wrote:
Scott W wrote: Roger N. Clark (change username to rnclark) wrote: There are often questions about smaller versus larger pixels and the corresponding camera size. Many of us would like smaller cameras that did just as good a job as larger ones. Is that possible? No, at least in terms of signal-to-noise that can be recorded. Here is why. There is a common idea in photography that exposure doesn't change between different size cameras when at the same f/ratio. For example, the sunny f/16 rule says a good exposure for a daylight scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100 second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16, a 35mm camera at f/16, an APS-C digital camera at f/16, down to the smallest point and shoot camera at f/16 (assuming the small camera goes to f/16). This leads people to think cameras scale easily and still give the same image. But there is a fallacy in this idea, and that is spatial resolution on the subject. The smaller camera, even at the same f/ratio, has a smaller lens which collects a smaller number of photons per unit time. The smaller camera gets the same exposure time because the UNIT AREA in the focal plane represents a larger angular size on the subject. The rate of arrival of photons in the focal plane of a lens per unit area per unit time is proportional to the square of the f-ratio. Corollary: if you keep f/ratio constant, and change focal length then the photons per unit area in the focal plane is constant but spatial resolution changes. So how does this apply to making smaller cameras? The problem is that if you scale a camera down, say 2x, the aperture drops by 2x, the focal length drops by 2x (to give the same field of view), the sensor size drops by 2x, and the pixel size drops by 2x (to give the same spatial resolution on the subject). It should be obvious by this point that per unit time the aperture has collected only 1/4 the number of photons. Also, the smaller pixels each collect 1/4 less photons since their area is divided by 4 to keep spatial resolution constant. Another way to look at the problem is aperture collects light, the focal length spreads out the light, and the pixels are buckets that collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE (ignoring transmission losses of the optics). Back to the camera example: scale a camera down by 2x keeping f/ratio and spatial resolution constant. You lose 4x the photons entering the lens with the smaller camera, and since you you must use 2x smaller pixels, the area is 4x less, so you LOSE ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a given resolution on the subject goes as the 4th power of the aperture (and camera size)! Decreasing your camera by 2x means 16x less photons per pixel if you want to maintain field of view and megapixel count! I believe you are off on this one. For the same f/number the photon flux at the sensor is the same. Take your case of scaling down a camera by a factor of two, the lens collects 1/4 the photons but it also spreads these photons out over 1/4the area that the larger camera does. The number of photons per sensor is therefor scales as the area of the sensor. So I believe you are looking at a 2nd power decrease not 4th. Scott Scott, You are correct. I forgot to include that for the smaller lens at half the focal length, the area on the subject doubles, canceling one of the squared terms. So, yes, I agree that the relation scales as the square not as the 4th power. So halving the camera size means pixels get 1/4 the photons. A good example is the Canon 20D with 6.4 micron pixels and a maximum signal at ISO 100 of 50,000 electrons, compared to the Canon S60 with 2.8 micron pixels with a maximum signal of about 11,000 electrons at ISO 100. The pixel size is 6.4^2 / 2.8^2 = 5.2x scaling, similar to the 50000/11000 = 4.5 scaling of maximum recorded signal. Then, for photon noise limited systems, signal-to-noise ratio scales as the square root of the camera size. Would not the S/N ratio scale with the size of the camera. If I make pixels with twice the linear dimensions I get 4 time the photons but only 2 times the noise for a gain of 2 in S/N. Scott |
#8
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The f/ratio myth and camera size
Roger N. Clark (change username to rnclark) wrote:
Scott W wrote: Roger N. Clark (change username to rnclark) wrote: There are often questions about smaller versus larger pixels and the corresponding camera size. Many of us would like smaller cameras that did just as good a job as larger ones. Is that possible? No, at least in terms of signal-to-noise that can be recorded. Here is why. There is a common idea in photography that exposure doesn't change between different size cameras when at the same f/ratio. For example, the sunny f/16 rule says a good exposure for a daylight scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100 second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16, a 35mm camera at f/16, an APS-C digital camera at f/16, down to the smallest point and shoot camera at f/16 (assuming the small camera goes to f/16). This leads people to think cameras scale easily and still give the same image. But there is a fallacy in this idea, and that is spatial resolution on the subject. The smaller camera, even at the same f/ratio, has a smaller lens which collects a smaller number of photons per unit time. The smaller camera gets the same exposure time because the UNIT AREA in the focal plane represents a larger angular size on the subject. The rate of arrival of photons in the focal plane of a lens per unit area per unit time is proportional to the square of the f-ratio. Corollary: if you keep f/ratio constant, and change focal length then the photons per unit area in the focal plane is constant but spatial resolution changes. So how does this apply to making smaller cameras? The problem is that if you scale a camera down, say 2x, the aperture drops by 2x, the focal length drops by 2x (to give the same field of view), the sensor size drops by 2x, and the pixel size drops by 2x (to give the same spatial resolution on the subject). It should be obvious by this point that per unit time the aperture has collected only 1/4 the number of photons. Also, the smaller pixels each collect 1/4 less photons since their area is divided by 4 to keep spatial resolution constant. Another way to look at the problem is aperture collects light, the focal length spreads out the light, and the pixels are buckets that collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE (ignoring transmission losses of the optics). Back to the camera example: scale a camera down by 2x keeping f/ratio and spatial resolution constant. You lose 4x the photons entering the lens with the smaller camera, and since you you must use 2x smaller pixels, the area is 4x less, so you LOSE ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a given resolution on the subject goes as the 4th power of the aperture (and camera size)! Decreasing your camera by 2x means 16x less photons per pixel if you want to maintain field of view and megapixel count! I believe you are off on this one. For the same f/number the photon flux at the sensor is the same. Take your case of scaling down a camera by a factor of two, the lens collects 1/4 the photons but it also spreads these photons out over 1/4the area that the larger camera does. The number of photons per sensor is therefor scales as the area of the sensor. So I believe you are looking at a 2nd power decrease not 4th. Scott Scott, You are correct. I forgot to include that for the smaller lens at half the focal length, the area on the subject doubles, canceling one of the squared terms. So, yes, I agree that the relation scales as the square not as the 4th power. So halving the camera size means pixels get 1/4 the photons. A good example is the Canon 20D with 6.4 micron pixels and a maximum signal at ISO 100 of 50,000 electrons, compared to the Canon S60 with 2.8 micron pixels with a maximum signal of about 11,000 electrons at ISO 100. The pixel size is 6.4^2 / 2.8^2 = 5.2x scaling, similar to the 50000/11000 = 4.5 scaling of maximum recorded signal. Then, for photon noise limited systems, signal-to-noise ratio scales as the square root of the camera size. Would not the S/N ratio scale with the size of the camera. If I make pixels with twice the linear dimensions I get 4 time the photons but only 2 times the noise for a gain of 2 in S/N. Scott |
#9
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The f/ratio myth and camera size
Hello Scott.
I have an issue with the following statement. also spreads these photons out over 1/4the area that the larger camera does. Now I am not overly well versed in the compromises made in the design photographic optics, but I can tell you that in difraction limited astronomical optics the angular resolution increases ( diffraction disk diameter decreases) in proportion to the diameter of the objective. This means that if you double the objective (lens/mirror) diameter and maintain the f-ratio, the diffraction disk remains a constant size. I recognise that this is counter-intuitive but it is determined by wave diffraction theory. Do a Google on "f +ratio +diffraction +disk +size" and you will find that this subject is well covered, particulary in photographic terms. I only looked at this one and it seems to be quite useful. http://www.cambridgeincolour.com/tut...hotography.htm Regards Ian On Sun, 05 Feb 2006 18:49:15 -0800, Scott W wrote: Roger N. Clark (change username to rnclark) wrote: There are often questions about smaller versus larger pixels and the corresponding camera size. Many of us would like smaller cameras that did just as good a job as larger ones. Is that possible? No, at least in terms of signal-to-noise that can be recorded. Here is why. There is a common idea in photography that exposure doesn't change between different size cameras when at the same f/ratio. For example, the sunny f/16 rule says a good exposure for a daylight scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100 second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16, a 35mm camera at f/16, an APS-C digital camera at f/16, down to the smallest point and shoot camera at f/16 (assuming the small camera goes to f/16). This leads people to think cameras scale easily and still give the same image. But there is a fallacy in this idea, and that is spatial resolution on the subject. The smaller camera, even at the same f/ratio, has a smaller lens which collects a smaller number of photons per unit time. The smaller camera gets the same exposure time because the UNIT AREA in the focal plane represents a larger angular size on the subject. The rate of arrival of photons in the focal plane of a lens per unit area per unit time is proportional to the square of the f-ratio. Corollary: if you keep f/ratio constant, and change focal length then the photons per unit area in the focal plane is constant but spatial resolution changes. So how does this apply to making smaller cameras? The problem is that if you scale a camera down, say 2x, the aperture drops by 2x, the focal length drops by 2x (to give the same field of view), the sensor size drops by 2x, and the pixel size drops by 2x (to give the same spatial resolution on the subject). It should be obvious by this point that per unit time the aperture has collected only 1/4 the number of photons. Also, the smaller pixels each collect 1/4 less photons since their area is divided by 4 to keep spatial resolution constant. Another way to look at the problem is aperture collects light, the focal length spreads out the light, and the pixels are buckets that collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE (ignoring transmission losses of the optics). Back to the camera example: scale a camera down by 2x keeping f/ratio and spatial resolution constant. You lose 4x the photons entering the lens with the smaller camera, and since you you must use 2x smaller pixels, the area is 4x less, so you LOSE ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a given resolution on the subject goes as the 4th power of the aperture (and camera size)! Decreasing your camera by 2x means 16x less photons per pixel if you want to maintain field of view and megapixel count! I believe you are off on this one. For the same f/number the photon flux at the sensor is the same. Take your case of scaling down a camera by a factor of two, the lens collects 1/4 the photons but it also spreads these photons out over 1/4the area that the larger camera does. The number of photons per sensor is therefor scales as the area of the sensor. So I believe you are looking at a 2nd power decrease not 4th. Scott |
#10
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The f/ratio myth and camera size
Scott W wrote:
Roger N. Clark (change username to rnclark) wrote: Scott W wrote: Roger N. Clark (change username to rnclark) wrote: There are often questions about smaller versus larger pixels and the corresponding camera size. Many of us would like smaller cameras that did just as good a job as larger ones. Is that possible? No, at least in terms of signal-to-noise that can be recorded. Here is why. There is a common idea in photography that exposure doesn't change between different size cameras when at the same f/ratio. For example, the sunny f/16 rule says a good exposure for a daylight scene is 1/ISO at f/16. Thus for ISO 100 film, you use a 1/100 second exposure on an 8x10 camera at f/16, a 4x5 camera at f/16, a 35mm camera at f/16, an APS-C digital camera at f/16, down to the smallest point and shoot camera at f/16 (assuming the small camera goes to f/16). This leads people to think cameras scale easily and still give the same image. But there is a fallacy in this idea, and that is spatial resolution on the subject. The smaller camera, even at the same f/ratio, has a smaller lens which collects a smaller number of photons per unit time. The smaller camera gets the same exposure time because the UNIT AREA in the focal plane represents a larger angular size on the subject. The rate of arrival of photons in the focal plane of a lens per unit area per unit time is proportional to the square of the f-ratio. Corollary: if you keep f/ratio constant, and change focal length then the photons per unit area in the focal plane is constant but spatial resolution changes. So how does this apply to making smaller cameras? The problem is that if you scale a camera down, say 2x, the aperture drops by 2x, the focal length drops by 2x (to give the same field of view), the sensor size drops by 2x, and the pixel size drops by 2x (to give the same spatial resolution on the subject). It should be obvious by this point that per unit time the aperture has collected only 1/4 the number of photons. Also, the smaller pixels each collect 1/4 less photons since their area is divided by 4 to keep spatial resolution constant. Another way to look at the problem is aperture collects light, the focal length spreads out the light, and the pixels are buckets that collect the light in the focal plane. BUT THE TOTAL NUMBER OF PHOTONS DELIVERED TO THE FOCAL PLANE IS ONLY DEPENDENT ON APERTURE (ignoring transmission losses of the optics). Back to the camera example: scale a camera down by 2x keeping f/ratio and spatial resolution constant. You lose 4x the photons entering the lens with the smaller camera, and since you you must use 2x smaller pixels, the area is 4x less, so you LOSE ANOTHER 4x photons/pixel. Thus, photons delivered to a pixel for a given resolution on the subject goes as the 4th power of the aperture (and camera size)! Decreasing your camera by 2x means 16x less photons per pixel if you want to maintain field of view and megapixel count! I believe you are off on this one. For the same f/number the photon flux at the sensor is the same. Take your case of scaling down a camera by a factor of two, the lens collects 1/4 the photons but it also spreads these photons out over 1/4the area that the larger camera does. The number of photons per sensor is therefor scales as the area of the sensor. So I believe you are looking at a 2nd power decrease not 4th. Scott Scott, You are correct. I forgot to include that for the smaller lens at half the focal length, the area on the subject doubles, canceling one of the squared terms. So, yes, I agree that the relation scales as the square not as the 4th power. So halving the camera size means pixels get 1/4 the photons. A good example is the Canon 20D with 6.4 micron pixels and a maximum signal at ISO 100 of 50,000 electrons, compared to the Canon S60 with 2.8 micron pixels with a maximum signal of about 11,000 electrons at ISO 100. The pixel size is 6.4^2 / 2.8^2 = 5.2x scaling, similar to the 50000/11000 = 4.5 scaling of maximum recorded signal. Then, for photon noise limited systems, signal-to-noise ratio scales as the square root of the camera size. Would not the S/N ratio scale with the size of the camera. If I make pixels with twice the linear dimensions I get 4 time the photons but only 2 times the noise for a gain of 2 in S/N. Scott Scott, I think you have clearly demonstrated that I should not do math and watch the superbowl at the same time ;-). Yes, you are correct. Roger |
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