The Physics of Digital Cameras

[Jonathan Ratzlaff]

Your argument is starting to sound a lot like xeno's paradox.  Unfortunately like xeno's paradox although it  seems to stand up under mathematical study, if falls down immediately the hare passes the toiroise.   So normally if a model is not supported by observation, then it is time to re-examine the model.

[PierreVandevenne]

The critical point here is that you can't brighten an image using optics alone, not with a lens that is designed to focus. If the distant sky is the same brightness through the lens as it is without the lens, then it is safe to say that the sun also will be no brighter. Why it burns the paper is an interesting question.

Really? May I suggest you release a paper about "The Physics of Burning Paper". You still have four months to April 1st.

[Jonathan Wienke]

Whether the sun is in sharp focus at the EXACT point of burning is an interesting question. No doubt most readers would think that it is, but consider this: Put your magnifying glass on its side your window ledge so that the lens is against the glass and look at something distant (not the sun). No matter how close or far you stand from the lens the scene is the same brightness with or without the lens.

This is easily disproven with simple experiments. If you take a magnifying lens and use it to focus the sun on an object, it is easy to verify experimentally that the highest temperature is reached when the image of the sun is focused to the smallest possible diameter (which happens to coincide with most people's definition of "sharpest focus").

The "equal brightness" claim is equally absurd. If you look through the viewfinder of a SLR/DSLR wearing a fast lens, (say f.1.2 or larger aperture), it is possible for the viewfinder image to be brighter than the subject. And as every beginner photographer knows, by adjusting the aperture (which changes the effective diameter of the lens), it is possible to create any brightness level desired within the adjustment range of the lens.

The same principle is true of any number of high-end rifle scopes with large objective lenses; a good-quality scope can create an image that is brighter than looking at the subject directly. They are larger, heavier, bulkier, and far more expensive than scopes with smaller objective lenses, but if you need to shoot in dim light, there is a world of difference.

The critical point here is that you can't brighten an image using optics alone, not with a lens that is designed to focus. If the distant sky is the same brightness through the lens as it is without the lens, then it is safe to say that the sun also will be no brighter. Why it burns the paper is an interesting question.

An interesting question indeed; the obvious answer is that your understanding of optics is fundamentally flawed. Contrary to your assertions, the image can be either brighter or dimmer than the original subject, depending on the quality of the anti-reflective coatings on the optical elements, and the ratio of aperture to focal length. The larger the diameter of the aperture relative to focal length, the brighter the image drawn by the lens will be. If the aperture is larger than the focal length (e.g. an f/0.5 lens), the focused image will be quite a bit brighter than the original subject, because the surface area of the aperture is greater than the surface area of the focused image. Such lenses are bulky, heavy, and very expensive, but they do exist, and they can passively amplify light by concentrating photons collected from a large surface area into a smaller surface area.

Night vision goggles use electronics to amplify light because an f/0.0625 lens would be as large as a Spartan's shield, weigh more than all of a soldier's other gear combined, be difficult to engineer to focus an acceptably distortion-free image, cost more than most houses, and have a depth of field so shallow as to be completely useless at distances less than infinity.

It is an interesting fact that many things in this world don't work the way you might think. Light amplification is one of them, academic peer review is another.

And you are demonstrably clueless about both.

[brianc1959]

Night vision goggles use electronics to amplify light because an f/0.0625 lens would be as large as a Spartan's shield, weigh more than all of a soldier's other gear combined, be difficult to engineer to focus an acceptably distortion-free image, cost more than most houses, and have a depth of field so shallow as to be completely useless at distances less than infinity.

The real reason you wouldn't want an f/0.0625 lens is that you can't simultaneously correct spherical aberration and coma in any lens faster than f/0.5.  This is due to a breakdown of the Abbe sine condition when the marginal ray angle exceeds 90 degrees.

[Plekto]

If they were using another material other than glass, though, that would change.  The question, though, is, what other materials would we possibly use besides glass and plastic?

[brianc1959]

If they were using another material other than glass, though, that would change.  The question, though, is, what other materials would we possibly use besides glass and plastic?

I'm not sure what you are referring to, but in case it was to my previous post the sine condition is not affected by the optical materials you use.

[WarrenMars]

Here is a photo of the sun's image correctly focused onto a piece of paper.



Note that the sun's image is NOT a small circle and it does NOT burn the paper.

The point where the rays meet may be the focal point for the lens but it is not the point at which the image is in sharp focus.
I would hope that when a photographer talks about focus he is talking about the subject being a clear image and not whether that image is as small as possible.

[brianc1959]

Here is a photo of the sun's image correctly focused onto a piece of paper.



Note that the sun's image is NOT a small circle and it does NOT burn the paper.

The point where the rays meet may be the focal point for the lens but it is not the point at which the image is in sharp focus.
I would hope that when a photographer talks about focus he is talking about the subject being a clear image and not whether that image is as small as possible.

Damn, Warren - I never realized that the sun was shaped like a football!  This is a major discovery!  You should publish it!

By the way, any idea what a severely defocused point image looks like when vignetting is present?

[Jonathan Ratzlaff]

By the way that is a projected image, and is related to the focal length of the lens that is producing it.  You may want to look at the telescope that is producing that image to find out how much of the objective lens is covered to ensure that the screen doesn't catch fire.  There are thousands of solar reflectors around that disprove your comments.
I think this discussion is best described by the phrase, " not even wrong"

An apparently scientific argument is said to be not even wrong if it is based on assumptions that are known to be incorrect, or on theories that cannot be falsified or used to predict anything. In science and philosophy, the second meaning is known as the principle of falsifiability.

The phrase was coined by the early quantum physicist Wolfgang Pauli, who was known for his colorful objections to incorrect or sloppy thinking.[1] Rudolf Peierls writes that "a friend showed [Pauli] the paper of a young physicist which he suspected was not of great value but on which he wanted Pauli's views. Pauli remarked sadly, 'It is not even wrong.' "[2]

[Jonathan Wienke]

Here is a photo of the sun's image correctly focused onto a piece of paper.



Note that the sun's image is NOT a small circle and it does NOT burn the paper.

The point where the rays meet may be the focal point for the lens but it is not the point at which the image is in sharp focus.

This is merely one more demonstration of your ignorance. In the configuration you show, the telescope is acting as a projector, not as a camera. The optics in a projector are designed differently than camera lenses; the imaging area is expanded to a far larger area than any camera sensor or film before it is focused. This image expansion is what prevents the image surface from burning, not the fact that the image is in focus. If you used a camera lens (which is designed to focus the image on a very small area) instead of the telescope (which is designed to focus the image on a large area), you'll discover that when the sun is in proper focus, its image will occupy the smallest possible area, and will definitely burn absorptive objects on the plane of focus.

[col]

Think the sun is in focus when you can burn paper with a magnifying glass do you? You've obviously NEVER done any solar observing using a telescope!

Warren,

It's great to see people like yourself thinking about physics, and how things work. Unfortunately you are wrong on a number of very basic points, including this one. You previously said that those that did not agree should "put up or shut up", and I agree entirely. I have no interest in making insulting remarks, and your academic qualifications are irrelevant. I prefer to judge only on the basis of your claims, so let's start with your claim that the sun is not in focus when paper is burned  with a magnifying glass.  

Forget for the moment about using a telescope. Your "paper burning" claim has to do with the opertaion of a simple magnifying glass, not a telescope.

Almost every schoolboy has burned paper with a magnifying glass and, as it turns out, the smallest and hottest spot on the paper corresponds to a focussed image of the sun on the paper. This is easily shown with a ray tracing diagram, for which I refer you to any basic text book.  

Ray tracing and trigonometry leads to derivation of the well know lens formulae. It is interesting to calculate the expected image size of the sun on the said sheet of paper. to see if the calculated prediction is in accordance with observation.

The lens formula is :-

1/u + 1/v = 1/f   where

u is the distance from the object (the sun) to the lens
v is the distance from the image to the lens
f is the lens focal length

Any units of distance can be used, such as meters, so long as the same units are used throughout. A typical magnifying glass has a focal length of 200mm, or 0.20m. So f=0.20

The distance from the sun to the earth is 150 million km, or 150E9 (m) So u=150E9

The first step in calculations is to find the distance from the lens to the image, that is, to find "v" in the above expression. As the object distance is effectively infinity, the term "1/u" is effectively zero, so "v" must equal "f". (ie, v=0.20m) In other words, for an object at infinity, the image will be located at the focal point of the lens. So far this seems roughly consistent with experience when burning paper, but let us continue, and calculate the expected image size.

The required formula (from any textbook)  is :-

Image Size = (hv)/u  where :-

h is the size of the object, in this case the diameter of the sun
h = 1.39 million km, or 1.39E9 (m)

Image size= (1.39E9 x 0.20) / 150E9
Image size = 0.00185 meters
Image size = 1.85mm


Hmmm. As an experienced paper burner, that is pretty much what I observe. With a typical magnifying lens having a focal length of 200mm, the hot spot on the paper (equals the focussed image of the sun) is around 1.8mm in diameter, and could be anywhere from around 1mm to 3mm depending on the focal length of the particular magnifying lens. The conventional optical theory really does seem to be right, does it not Warren? The ball is in your court.

Cheers, Colin






 

[Slobodan Blagojevic]

... With a typical magnifying lens having a focal length of 200mm, the hot spot on the paper (equals the focussed image of the sun) is around 1.8mm in diameter...

I have no degree in physics, but what Colin is saying seems to be in line with a rule of thumb I heard long time ago regarding photographing sunsets/sunrises: the sun image on the film/sensor will be approximately 1/100 of the focal length. In other words, if you are a shooting with a 200 mm telephoto, the sun size will be approximately 2 mm. In order to fill the frame (24x36 mm), one would need a 2400 mm telephoto.

[WarrenMars]

Image size= (1.39E9 x 0.20) / 150E9
Image size = 0.00185 meters
Image size = 1.85mm

Hmmm. As an experienced paper burner, that is pretty much what I observe. With a typical magnifying lens having a focal length of 200mm, the hot spot on the paper (equals the focussed image of the sun) is around 1.8mm in diameter, and could be anywhere from around 1mm to 3mm depending on the focal length of the particular magnifying lens. The conventional optical theory really does seem to be right, does it not Warren? The ball is in your court.

Cheers, Colin

Ok, folks, it is time for me to eat some humble pie, and I am happy to admit I was wrong about the sun's image not being at the focus during magnifying glass burning. I am familiar with the thin lens equation and it seems obvious in retrospect that I should have checked it, but when one is hot on the trail of a theory one tends to pay less attention to counter evidence than one ought. Mea culpa. Thank you Colin, I shall correct my website.

The telescope projection had a magnification of about 40x which explains the size difference over the magnifying glass which actually reduces the size of distant objects. There is no problem comparing telescopes, cameras and magnifying glasses in this matter, they all produce real images.

I now see why it is that the image burns, even though everything to the eye seems to be the same brightness with and without the lens. It is because the eye itself is not at the focus but back a comfortable distance. This stepping back to allow the eye's own optics to refocus the image allows the image brightness to dissipate, returning the brightness to "normal". Someone else may like to do the maths to demonstrate why it is that it should be EXACTLY normal.

As for the question of light amplification through optics alone, I believe the above effect may have something to say about its limitations when it comes to the human eye. I appreciate your comments on the subject Jonathon, but I must say that for the time being I am not convinced. When I use my f/2.8 lens I don't see a noticeable improvement in brightness over my f/5.6 even though according to you there should be a difference of 2 STOPS. I do see some attenuation over reality in both lenses but this I tend to put down to losses in the various mirrors. Yes, I should like the opportunity to test out a nice f/0.5 prime but strangely I just can't seem to source one.

Happy New Year to those of good will!

[Jeremy Payne]

Some more interesting content from our new friend Warren Mars ...

http://www.unemployedaustralia.org/

http://www.unemployedaustralia.org/about/wmars.htm

[joofa]

Some more interesting content from our new friend Warren Mars ...

Jeremy, there is no need for personal attacks. Warren has already admitted one of his errors. It is always appreciative when one admits mistakes in understanding on a public forum. There are so many others on this forum who just don't admit they are wrong. For a proof look no farther than dpreview.com where everybody thinks they are an expert and there is so much uninformed "camera theory" flying around ...

 Remember the 3 golden words: "I don't know."

[Jeremy Payne]

Jeremy, there is no need for personal attacks.

I put a link to his website so we could all have some additional background information.  He put it out there ... not me ...

How is that a personal attack?

[Jeremy Payne]

...

Just be thankful I didn't link the porn, pardon me - "Ribauld Verse" - from his other website.

[Jonathan Ratzlaff]

Even when something is off the wall so to speak, it always helps to think about it a bit to see whether there is some truth in what is being stated.  This has been a fairly lively discussion as to some of the nature of optics.  Even when there are errors, it still has been an interesting exercise.

[col]

The critical point here is that you can't brighten an image using optics alone, not with a lens that is designed to focus.

When I use my f/2.8 lens I don't see a noticeable improvement in brightness over my f/5.6 even though according to you there should be a difference of 2 STOPS.

The first thing to realize is that the human eye must be removed totally from the discussion. The discussion pertains to digital cameras, where a lens projects a focussed image onto a CCD detector at the image plane. Therefore when Warren talks about "brigtness of an image", he is talking about the brightness of the image on the camera CCD. The units of brighness, AKA intensity, in this context is photons/second/unit_area.

As Warren has realized, we don't place our eye at the CCD image plane, and would learn nothing useful if we did, so Warren's previous observations involving looking through magnifying glasses at the sky are irrelevant. At the risk of being repetitious, the question is whether the image on a digital camera CCD can be be made brighter using optics alone.

To be even more precise, Warren apparently claims that an F2.8 lens does not produce a brighter image thanan F5.6 lens, and that claim is incorrect.

Fnumber is defined as the focal length divided by the aperture diameter.  Fnumbers are used precisely because for a given scene, the image intensity depends only on the Fnumber, assuming no losses in the optics.  Halving the Fnumber increases the image intensity by a factor of four (2 stops), and that's all there is to it. As every photographer knows, if the Fnumber is halved while the shutter speed and ISO are left unchanged, the image will indeed be much brighter, in fact hopelessly overexposed if the exposure was correct at the higher ISO.

I suspect Warren will agree in hindsight that all of the above is correct, and that the image can indeed be made brighter by fitting a faster lens with smaller Fnumber.

Cheers, Colin

[bjanes]

The same principle is true of any number of high-end rifle scopes with large objective lenses; a good-quality scope can create an image that is brighter than looking at the subject directly. They are larger, heavier, bulkier, and far more expensive than scopes with smaller objective lenses, but if you need to shoot in dim light, there is a world of difference.

This brings up an interesting point. A scope with a larger objective collects more light, but the eye can use this property only up to a certain limit. When you look through a telescope or microscope, you place your eye at the exit pupil of the eyepiece. The exit pupil or eyepoint can be found by placing a transparent sheet of paper in front of the eyepiece and adjusting the position of the paper until you get the smallest illuminated circle. The specimen is not in focus at the eyepoint and you are looking at a a virtual image. If you place a ground glass at the eyepoint, you will simply get a circle of light with no image detail. If you move the glass back in a darkened room, you will get a real image.

With a binocular of telescopic sight, the size of the exit pupil can be found by dividing the objective diameter by the magnification. Then the exit pupil is larger than the diameter of the pupil of the observer's eye, the extra light gathering power of the instrument can not be used. See here. This may be what Warren is talking about.

If you use a magnifying glass to examine a small object, you are looking at a virtual image, but if you use it as a burning glass, you are focusing an image of the sun at the focal point of the lens. For a given focal length, the size of the imaged disc will be the same, but the intensity will vary with the square of the diameter of the lens.