F-Ratio and brightness

[JoLo]

That is the way I understood them to work, but I am no camera expert, and have been wrong on more than one occassion....this week. When you put it like that, it does make sense.

I was thinking of lenses that do not have a constant f stop, but vary within a range when zoomed. Isn't that just a function of the aperture being stopped down or up? With a constant focal ratio though, my reasoning breaks down, doesn't it?

[ollypenrice]

Hi Olly

I think what you are missing here is that in both cases the same amount of light from M51 hits the chip as the aperture is the same (assuming that M51 falls entirely within the FOV) however on the shorter focal length (faster scope) this is shared between fewer image receptors (pixels) and therefore a given exposure (number of photons hitting a receptor) is achieved in a shorter time.)

Clear skies

Paul

Indeed, Paul, but what happens when you screen-enlarge the small M51 from short FL to the same size as the larger M51 from the long FL? From where do you conjour any benefit? This is the F ratio myth and the subject of my paragraph.

Olly

[LDUNN1]

....well you do get zooms that vary their aperture as they zoom, but many maintain their aperture throughout their range.

....I've never thought of the maths involved before.....the only way you can have f2.8 at 200mm AND f2.8 at 70mm on the same zoom is if the effective diameter of the front element varies.

.....if the effective diameter of the front objective stays constant then 70/71.5 = f0.98!

......just when I thought I understood something.....;-)

[ollypenrice]

Camera speak belongs in the astronomical dustbin. It is a soup of rich confusion!

Stick to FL, FR and aperture in stage one.

In stage two, more complicated, introduce pixel size. (If you feel you really have to!!)

Olly

[DoctorD]

Hi Olly

Post exposure magnification does not spread the captured electrons anymore thinly across the image - then core of a M51 would still

have the same pixel values (I.e exposure).

What you do get is a lower spatial resolution.

So if your aim is to take an image and get the brightest part if the subject to a 90% exposure level - say 220 on an 8 bit CCD this would be achieved 4 times quicker on an 200mm F5 than a 200mm F10 scope using the same image sensor albeit the image scale would be smaller.

Then again, I'm so confused now I could be wrong

Clear skies

Paul

[dph1nm]

Post exposure magnification does not spread the captured electrons anymore thinly across the image - then core of a M51 would still

have the same pixel values (I.e exposure).

What you do get is a lower spatial resolution.

So if your aim is to take an image and get the brightest part if the subject to a 90% exposure level - say 220 on an 8 bit CCD this would be achieved 4 times quicker on an 200mm F5 than a 200mm F10 scope using the same image sensor albeit the image scale would be smaller.

I probably shouldn't get involved in these discussions again, but note that although post exposure magnification does not do anything for you, post exposure de-magnfication does increase the signal-noise per pixel (if you do it right). Hence the slower f10 can be de-magnified to give the same signal-noise per same-sized pixel (in arcsec) in the same exposure time as the f5. Hence the f-ratio myth.

NigelM

[LDUNN1]

Hi Nigel, can you explain this to me somemore:-

"slower f10 can be de-magnified to give the same signal-noise per same-sized pixel (in arcsec) in the same exposure time as the f5"

I don't think I understand.......& your point seems to be very relevant & interesting......how would you go about the 'de-magnify' process in something like photoshop?

[dph1nm]

slower f10 can be de-magnified to give the same signal-noise per same-sized pixel (in arcsec) in the same exposure time as the f5

If you bin up pixels in software (so take a block of 2x2 pixels and average them together to form one 'super' pixel) you will recover the signal-to-noise you would have had if you had exposed with a CCD with pixels that size in the first place (providing your small pixels are not dominated by read noise). Essentially this is the same as on-chip binning (except read noise is not then an issue at all).

So if you exposure for the same time with all these setups you will get the same depth of image:

200mm f5 + CCD with 5um pixels

200mm f10 + CCD with 10um pixels

200mm f10 + CCD with 5um pixels on chip binned 2x2

200mm f10 + CCD with 5um pixels 2x2 averaged in software

For colour cameras this is all a bit tricky due to the bayer matrix (you could do it by binning the RGB channels separately then reforming the bayer pattern, but I don't know of any software that does), but for mono ones it is quite simple (BTW you must do it before you do any post processing e.g. stretching of the image).

I don't use Photoshop, but GIMP has an option for block averaging like this, so I imagine Photoshop does.

NigelM

[great_bear]

I think I got my head around it a few posts back (the long one I made), so all's well unless I fundamentally misunderstood something.

I think the problem is that some people just aren't very good at stating exactly what they mean. They blame the reader for the confusion that the writer caused by their poorly-written, half-explanations. In this instance, the confusion could have been avoided if the explanation had said: "For a given magnification, F-Ratio has no effect on brightness."

[studio1one]

Thanks to all for you answers - I believe you got me onto the right tracks and thinking this through carefully.

I know how you feel

Anyhow, as alluded to in some of the responses above, I believe the statement comes from the magnification factor. However, without a concrete example I couldn't get my head around it. So, I've been playing with figures, and this is what I now understand.

Important point 1 -

In the case of "prime focus" Astro Photography, the telescope itself acts as the lens, so everything we know about f-numbers and exposure times holds true.

Important point 2 -

When viewing visually, we add an eye piece to magnify the image produced by the telescope. The optics aren't the same as for AP above.

Objective

I'd like to understand this statement:

"For photography, faster f/4 of f/6 systems yield shorter exposure times. But when used visually, image brightness depends solely upon the aperture. Focal ratio has nothing to do with it."

So the objective is to demonstrate that only the diameter, and not the f-number, affects the brightness.

To demonstrate this I'm going to make the assumption that the viewer would like to see a given object at the same size on his retina (i.e. with the same total magnification compared to the naked eye), regardless of the telescope being used.

Proof part 1 - f-number doesn't affect brightness

Let's compare two hypothetical telescopes A and B:

A - Focal length = 800mm, Diameter = 200mm, F-Number = f/4

B - Focal length = 1600mm, Diameter = 200mm, F-Number = f/8

Note that:

1) the diameters are the same, the f-numbers are different

2) the field of view of telescope A is twice as big as telescope B.

3) telescope A collects four times as much light as telescope B (it's 2 stops faster)

With telescope A, the user chooses to magnify the image 100x (using a 8mm eyepiece).

With telescope B, the user only has to magnify by 50x (using a 32mm eyepiece) to see the image at the same size.

Since telescope A requires twice the magnification of B, it requires four times as much light to render the image at the same brightness (inverse square law). Since A collects four times as much light as B this achieved - the image brightness is the same even though the f-number has changed.

Proof part 2 - changing the aperture alone affects brightness

I'm sure the that rest will be obvious now, but we'll continue for completeness.

Let's compare two hypothetical telescopes C and D:

C - Focal length = 800mm, Diameter = 200mm, F-Number = f/4

D - Focal length = 1600mm, Diameter = 400mm, F-Number = f/4

Note that:

1) the diameters are different, the f-numbers are the same

2) the field of view of telescope C is twice as big as telescope D.

3) the two telescopes collect the same amount of light

With telescope C, the user chooses to magnify the image 100x (using a 8mm eyepiece).

With telescope D, the user only has to magnify by 50x (using a 32mm eyepiece) to see the image at the same size.

Since both telescopes have collected the same amount of light, the image created by telescope A will be 4 times dimmer than that created by telescope B since the image is being magnified twice as much.

The large aperture of telescope D results in a brighter image, even though the f-number has stayed the same.

QED.

Conclusion

So, to go back to the original quote:

"For photography, faster f/4 of f/6 systems yield shorter exposure times. But when used visually, image brightness depends solely upon the aperture. Focal ratio has nothing to do with it."

I think that this was what's intended:

"For photography, faster f/4 of f/6 systems yield shorter exposure times. But when used visually, for an object viewed at given final magnification (compared to the naked eye), image brightness depends solely upon the aperture. Focal ratio has nothing to do with it."

Under these conditions, the focal length of the telescope dictates only the field of view, and thus the eyepieces required to achieve a given object size. The diameter dictates brightness (and resolution). F-number holds little other value.

Disclaimer

I've read in several places that the only the aperture controls brightness for visual observing, and not once have I seen this qualified with "for a given magnification" (with the exception of Barry's post above of course), so maybe I'm on completely the wrong tracks here...

For example, here's Wikipedia's comments:

"Even though the principles of focal ratio are always the same, the application to which the principle is put can differ. In photography the focal ratio varies the focal-plane illuminance (or optical power per unit area in the image) and is used to control variables such as depth of field. When using an optical telescope in astronomy, there is no depth of field issue, and the brightness of stellar point sources in terms of total optical power (not divided by area) is a function of absolute aperture area only, independent of focal length. The focal length controls the field of view of the instrument and the scale of the image that is presented at the focal plane to an eyepiece, film plate, or CCD."

No mention of why that's the case, or of any assumptions about magnifaction.

Hmm.....

Unless I am mistaken, which is entirely possible your synopsis is incomplete.

An aperture of 200mm will collect the same amount of light, no matter the focal length. What will alter is the FOV that light is collected from. Ie the angle of the light entering the tube.

The aperture at the end of the scope has no knowledge of how long the tube behind it is, whether the tube behind is 1000mm or 2000mm the same amount of light will enter the tube.

Therefore a 200mm f4 scope will not collect 4x more light than a 200mm f6 scope, they will collect the same amount of light. What will change is the angle of light that can hit the secondary lens / primary mirror.

[great_bear]

Therefore a 200mm f4 scope will not collect 4x more light than a 200mm f6 scope, they will collect the same amount of light.

Hmmm... For a given magnification, yes, but for the "system" overall?

Surely it depends on how you're measuring this. For a longer tube, light that would have hit the mirror with a shorter scope, is now hitting the tube walls. Imagine replacing the mirror with a photovoltaic cell for the measurement of light-gathering, in order to see what I'm saying here.

[spanky]

I'm still puzzled, can someone help me out here?

Regardless of the difference in field of view, let's assume I'm going to crop the wider one so it matches the narrower one.

I have 6" f/5 and an 8" f/5 side by side with the same camera on each and both pointing at the same target.

I do one sub on each for, say 10 mins.

Which one gives me a brighter image? Or are they both the same?

[studio1one]

Hmmm... For a given magnification, yes, but for the "system" overall?

Surely it depends on how you're measuring this. For a longer tube, light that would have hit the mirror with a shorter scope, is now hitting the tube walls. Imagine replacing the mirror with a photovoltaic cell for the measurement of light-gathering, in order to see what I'm saying here.

Yes, I completely agree with you, this was what I was trying to get at by stating at the end

"What will change is the angle of light that can hit the secondary lens / primary mirror."

So the tube gathers the same amount of light but light from a narrower FOV is useable by the objective.

[studio1one]

Sorry, to be a little clearer, this is why I said his hypothesis was incomplete, rather than wrong. Both telescopes collect the same amount of light but in actual fact light from a narrower FOV is useable by one.

[great_bear]

I'm still puzzled, can someone help me out here?

Regardless of the difference in field of view, let's assume I'm going to crop the wider one so it matches the narrower one.

I have 6" f/5 and an 8" f/5 side by side with the same camera on each and both pointing at the same target.

I do one sub on each for, say 10 mins.

Which one gives me a brighter image? Or are they both the same?

Nice question.

Since they are both F5, the brightness is the same.

[spanky]

Nice question.

Since they are both F5, the brightness is the same.

Thanks!

So purely for photography if I upgraded from 6" f/5 to an 8" I'd have to get an f/4 to be able to image quicker in one session, rather than getting an f/5

Saved me and anyone else who reads this a few quid at some stage