# Light collection 42

Started Mar 3, 2020 | Discussions thread
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Light collection 42

After the many (vitriolic) threads I'll try one more time to try and clear things up.

In May of 2018 Andy Lucy asked some questions in this thread that went on until 3 months ago before I was occupied by real work. First I want to thank Andy for keeping calm and never attacking in that or any other thread, something I can't say for some others here. FYI I will periodically disappear and not answer a thread when I have pressing work that consumes my time, I am on a trip, or simply disgusted with the troll activity in a thread so I stop looking. It is not an indication that I agree with the many wrong concepts that may be touted in the thread, a fact that was prevalent in the above referenced thread.

In the above thread, this post: CEFA Again , Mark says:

CEFA reduces to the following simple relationship:

CEFA = k*exposure_time*sensor_area/(focal_ratio^2)

where k is some (easily calculated) constant

Andy and Mark get to this conclusion by saying angle is dimensionless (quiz below). They say lens aperture area is not a factor. Let's see that new equation works in practice.  All of this (I hope) should clear up misconceptions on light collection that have hampered this forum for a couple of years.

I'll hold exposure time constant (1/800 second), f-ratio constant (f/4) and derive the number of photons collected for different sensor sizes.

The firs 4 images below are all with a full frame sensor on the same object so the

k*exposure_time*sensor_area/(focal_ratio^2)

should be the same, thus the same amount of light. The main variable is lens aperture area, so if their equation is correct, we should get the same amount of light in each of the 4 images.  To get he light collected, I used the linear raw data and calibration of gain and corrected for offset.  The Moon images were all made on the same night within minutes of each other with the Moon high in the sky.

So we see that the average light per pixel changed, the total light per frame changed, and the total light from the object (the Moon) changed. There are 2 variables that changed: focal length and lens aperture area (lens transmission is similar in each case and differences are a small factor). Now, anyone who has used a light meter and short focal length lenses has experienced the variable exposure indicated when trying to photograph the Moon. Mark, have you tried that? Clearly Mark, your equations fails to predict the light collection. The Moon shines X photons per square meter onto the Earth, so it should be obvious from basic principles that the controlling factor in light collection is the lens aperture area, not sensor area, not f-ratio.

OK, now lets vary sensor size: a 2x crop sensor:

Gee, what happened? The proposed equation should indicate 2x less light, but total light from the frame is close to the same, the light from the Moon is the same within the noise, but the light per pixel is significantly more. Again, the proposed equation fails. Note too that the peak brightness increases from the 28 mm image to the 2x crop image.

Two more example, with changing sensor size, same f-ratio, exposure time and ISO as above.  Note the Moon is illuminated by the Sun, so are the two daytime images below, the first illuminated only by the Sun.  The second includes the Sun shining on the sea.

Again, Mark's equation predicts less light would be collected by the smaller sensor, but the above two images show significantly more light is collected, and even more light per pixel is collected.

The failure of the equation illustrates a flaw in the derivation.   To further illustrate the concepts, here is a quiz, mainly for Mark who is adamant about his equation, but anyone is welcome to respond.

Question: Can you reasonably image the following astrophotography situation?
You can choose lenses and mirrorless or dslr, cameras that are on the market.
What lenses, cameras and exposure times would you use?
According to the proposed equation, all the information you need is here.

Sky surface brightness = magnitude 17

Surface brightness:
object A1 = magnitude 28.0
object A2 = magnitude 19.1
object A3 = magnitude 14.2
object A4 = magnitude 10.2
object A5 = magnitude 1.4

Roger

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