Best DSLR or ILC for Night Sky Imaging?

Started Nov 8, 2017 | Questions thread
rnclark Senior Member • Posts: 3,755
Re: If you want the best, a dedicated cooled CCD cameras are far better than all the DSLRs and ILCs
8

kiwi2 wrote:

JimH123 wrote: One thing you are leaving out and that is stars are point sources of light, not extended objects. For them, the size of the objective, or mirror, is what is important, not the f-ratio.

Are the dpreview test scenes point source or extended objects? Perhaps you should explain the difference to Roger.

rnclark wrote:
"DPreview changes focal length while keeping f-ratio constant. That means lens aperture area changes between cameras, thus the light delivered to the sensor is changing, and that means the amount of photon shot noise is different due to the lens, not the sensor."

I see a lot of confusion here, so I'll try to help. The confusion is along multiple lines of thinking, including the inverse square law, light collection light density in the focal plane, and the amount of light from the subject. First some basic facts.

The inverse square law is always in effect and is not limited to just point sources.

Photography exposure (film or digital) is about light density in the focal plane but not total light from a subject.

The light collected by an optical system depends on the collection area of the system, technically the entrance pupil, commonly called the lens aperture area.

All situations are exactly described by the very simply equation:

system throughput = Etendue = A * Omega

A = entrance pupil area (lens aperture area)

Omega = solid angle of the **SUBJECT**

The first main problem in the discussion, mainly pushed by kiwi2 is focused
on light density averaged over the whole focal plane. This is the classical
photography view of exposure and f-ratio controlling the light density.
Side note: if this view were correct, astronomers would have no need to
build big telescopes. With the atmosphere limiting resolution, they would
just need a focal length to resolve an arc-second or so, e.g. 500 mm and then
make a fast system, like 500 mm f/1 and they could do no better. So why then
do they build telescopes like the U. Hawaii 2.23 meter aperture diameter
f/10 telescope? The simple answer is that the aperture area is key, not the f-ratio.
And the Etendue equation tells why.

The photographer exposure idea is f-ratio tells the amount of light delivered
to the focal plane and they give examples, sometimes with different focal lengths,
like 28 mm f/4 and 200 mm f/4 of the "same" scene showing the "brightness" is the
same. If you total all the light in the focal plane it will be the same. This is true but ignores a very important key fact: the subject is not the same with the two lenses!
With the change in focal length, the angle of view changed, so the scene recorded
is different, and the scenario only works if the scene is uniformly light, and technically
only works if the scene is exactly the same intensity everywhere, like a blank,
uniformly lit wall! Fortunately, the real world is more interesting than a uniformly-lit
blank wall.

Let's try an astronomy-related example: the full Moon in a dark night sky. Image the
full Moon with a variety of lenses with the same f-ratio and same exposure time.
I did this in Figure 4 here: http://www.clarkvision.com/articles/exposure/
(where this very subject is discussed). There, 3 images of the Moon are shown:
with 28 mm f/4, 70 mm f/4 and 200 mm f/4.

The key here is that the subject we view in the image is not an average of the
whole focal plane; it is specific subjects in the focal plane. The **SUBJECT**
is the Moon, not the entire frame. Or maybe we are interested in a crater on the
Moon, not the entire Moon. In that case the **subject** is the crater.

In regular photography the subject might be a bird in a tree, or a person's face in a
portrait. Do we have enough light to define the eye if the bird or the person in the portrait?  The eye could be considered the subject. It is the signal-to-noise of these subjects that is important for image quality, NOT the average scene brightness.

Back to the Moon

Let's consider the subject is the Moon and it shows as 33 pixels in diameter in
the 28 mm image. It would then be 82.5 pixels in diameter in the 70 mm image,
and 235.7 pixels in the 200 mm image. Again, see Figure 4 in the above reference.
If the average signal on the Moon, the photographic exposure, were 1000 photons per pixel, then we see that the total light **FROM THE SUBJECT**, the Moon, is:

28 mm image: 1000 *(pi/4) * 33^2 = 855,299 photons.

70 mm image: 1000 *(pi/4) * 82.5^2 = 5,345,616 photons.

200 mm image: 1000 *(pi/4) * 235.7^2 = 43,632,394 photons.

The 70 mm f/4 lens collected 5345616 / 855299 = 6.25 times more light than the 28 mm lens.

The 200 mm f/4 lens collected 43632394 / 855299 = 51 times more light than the 28 mm lens.

These ratios are the same as the lens aperture area ratios (exercise to compute that is left to the reader).

If by some magic the 28 mm lens was not limited by diffraction, and we shrunk
the pixel size on the camera with the 28 mm lens so it delivered an image of the
Moon 235.7 pixels across, we would have only about 19.6 photons per pixel and the image of the Moon would appear extremely noisy.

The key to image quality is collecting enough light for the image detail. Each piece
of image detail can be thought of as a subject.

The Etendue equations explains it: A * Omega: Omega for the Moon is 1/2 degree diameter, so the only factor in light collection from the Moon is lens aperture area (the entrance pupil). This is true for all other astronomical objects, and is also true for any subject at a fixed distance.

Now lets consider the inverse square law. If we got into a spaceship a traveled to half the distance to the Moon, the Moon would appear twice the diameter to our eyes and cameras, thus 4 times the angular area. Omega in the Etendue equation has now been increased by 4x, so our cameras collect 4x more light from the Moon, yet the exposure time for our sensors would be the same as our more distant position. The greater amount of light we collect allows us to make a more detailed image without increased noise.  So the change in the Omega variable describes the effect of the inverse square law.

Back to astronomers building big telescopes: it is to collect light. They understand that the f-ratio is not the key to collecting light, lens aperture area is. Example, some of my early work was measuring spectra of the the satellites of Jupiter and Saturn. I was using the U. Hawaii 2.2 meter aperture f/10 telescope. I needed more light, so I got time on the NASA IRTF 3.2 meter aperture telescope, at f/38, then on the United Kingdom 3.8-meter aperture telescope (UKIRT) at f/35. The larger aperture enabled me to collect more light. Good thing I didn't listen to photographers who would have told me that with f/38 I would get less light and not be able to get the data I wanted.

That was still not good enough, so then a group of us worked to employ the inverse square law. Good thing we didn't listen to photographers who would say the inverse square law does not apply to extended objects. We put together a 22.9 cm aperture (9-inch) Ritchey Cretien telescope, f/3.5 and it got sent to Saturn on the Cassini spacecraft. The inverse square law meant that we could collect enough light to measure small things on the satellites because we got around a million times closer, or 10^12 times more light than could be collected from earth with the same sized telescope.

Summary: look at total light from the subject. The subject can be a bird in a tree, the eye in that bird in the tree, the glint in the eye of the bird. The subject could be a person's face in a portrait, or a distant galaxy in the sky. The key is the subject, not average scene light density of a uniformly lit wall.

Focus on the subject, not the pixels.

More info on this subject is in my series starting here: http://www.clarkvision.com/articles/exposure/

The key is Etendue. Etendue has only two variables and that is fundamental: entrance pupil area and subject angular area. Etendue explains ALL situations regarding light collection from a subject.

Etendue also explains why a larger format camera collects more light when a lens is used that covers the same field of view as on a smaller format camera using the same f-ratio. Bonus: if you can apply Etendue and explain why it is not the sensor sensitivity, then you understand Etendue and why all those review sites online are wrong when they say a larger format sensor is more sensitive.

If you think this is all wrong (I've had similar arguments with many other photographers not able to see out of their box), please tell us where the math of Etendue is wrong. See https://en.wikipedia.org/wiki/Etendue and then tell us how with a faster f-ratio astronomers do not need to build big telescopes, and how they can do better with a smaller but faster lens to concentrate all that light. Then tell us how NASA can save billions of dollars because they don't understand the inverse square law. Do this and you will certainly win a Nobel prize.

If you do understand the Etendue, compute Etendue * exposure time for the test scenes where I said the light was varying.  It should then be obvious that the amount of light from a subject in each image is different.  The subject is the detail you view in any part of an image.

======

Now to visual observing. The eye does not operate like a camera. The eye is a contrast detector constantly adapting to brightness. As brightness drops, the combines signals from multiple receptors to make fainter detections. It is like dynamic binning. The eye also integrates a faint subject for 6 to 15 seconds. I wrote a whole book about this:

Clark, R.N., Visual Astronomy of the Deep Sky, Cambridge University Press and Sky Publishing, 355 pages, Cambridge, 1990.

(It is out of print, typical used prices are $200 and up.)

The bottom line is that the eye has optimum detection for the faintest subjects when the object to be detected is about 1/2 to 2 degrees across. The subject could be a galaxy, or a spiral arm in a galaxy, a spot on a planet, a bird in a tree. Again it has nothing to do with average scene brightness, or average intensity of a uniformly lit blank wall, ot f-ratio.

Because a smaller aperture telescope collects less light, objects are fainter, and being fainter, that requires higher magnification. Concentrating a faint object at low magnification results in seeing less detail on that faint object. This topic is discussed here:

http://www.clarkvision.com/articles/visastro/omva1/

Roger

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