Re: Etendue, f-number, and aperture diameter

Etendue, f-number, and aperture diameterHi,

yes, the Etendue of the big camera is just bigger.
The major implication is collection of more flux.

Kind regards
Joachim
"Michelle" <mhs.news@xxxxxxxxxxx> schrieb im Newsbeitrag news:000401c8c1d7$96710da0$48d07d80@xxxxxxxxxx
Thanks Joachim. This goes along with my initial thinking (that the irradiance is the same for both cases). However, I didn't think to compare what happens if you keep the number of pixels at the sensor plane constant for the two cases. That is helpful. I suppose, that since the SNR would be higher for the larger camera, then it would be reasonable to assume it would take better pictures in low light conditions than the smaller camera (at the same f-number and frame rate).



I am still wondering what the meaning of etendue is for these two cases. Am I correct that the etendue of the larger camera is bigger? What does this imply for an imaging system?



Michelle





From: Joachim Wietzorrek [mailto:wietzorrek@xxxxxxxxxx]
Posted At: Thursday, May 29, 2008 2:09 PM
Posted To: sci.optics
Conversation: Etendue, f-number, and aperture diameter
Subject: Re: Etendue, f-number, and aperture diameter



Hi Michelle,



the answer seems pretty simple to me:



Indeed, the brightness of both images will be the same.

At least if you consider brightness as irradiance. This is the optical flux divided by the area of image. This number (ratio) will be the same for both kinds of lenses you have described.



However, the big lens will collect more flux or also more photons. If you have the same number of pixels in both cases, the bigger camera will provide a better signal to noise ratio. Any of the pixels will detect more photons, even when the "brightness" is just the same.



In short term:

A big SLR camera will provide much nicer images than a lousy mobile phone camera, even when you use the same f-number.



Kind regards,

Joachim

"Michelle" <mhs.news@xxxxxxxxxxx> schrieb im Newsbeitrag news:000001c8c1c2$100f6640$48d07d80@xxxxxxxxxx

I am trying to better understand how image brightness varies for lenses with the same f-number and same angular field of view, but different diameters (apertures).

We are often "told" in optics that f-number controls image brightness (though a closer look shows that magnification also comes into play, but then I suppose you could say "working f-number controls image brightness). But it seems that the diameter of the lenses in otherwise equvalent f-number systems is important when you compute the etendue, which ultimately determines image brightness, right?

For example:

Assume you have two single-lens systems:

1. One lens is 10 times larger in diameter than the other.

2. Both lenses have the same f-number at infinite conjugates.

3. Both lenses have the same field of view (so the field stop or image height is larger for the larger lens).

4. Same source illumination (imagine a big, flat, perfectly lambertian source that overfills the aperture).

5. Neglect effects of aberrations, vignetting, relative illumination, and transmission losses.

Since the area of the bigger lens is 10 times that of the smaller lens, and they both have the same solid angle from the exit window to the exit pupil, a calculation of etendue shows that:

Etendue_bigger_lens = 100 * Etendue_smaller_lens

Does that sound right? Does the bigger lens produce a 100x brigher image? Or am I missing something? I can see that there would be more power (flux density) captured by the bigger lens, but it is spread over a larger area at the image plane. Is the irradiance at the image equal in both cases? Hmmmm.

By the way, I am ultimately thinking of image forming systems like digital cameras. I am wondering if a digicam with a larger lens produces a brighter image than a digicam with a much smaller lens, but at the same f-number. Initially I just want to think about this for large object distances, but then I would like to understand how this would work for objects closer to the lens, where the magnification gets close to 1.