Image Luminosity vs magnification

I think I recall several people saying that assuming same aperture and
same magnification, visual image brightness remains the same.

For different apertures, the ratio will be (assuming no obstruction)
D1/D2=pi*rho_1^2/(pi*rho_2^2) which reduces to (rho_1/rho_2)^2.

How does brightness/luminosity vary with magnification?

Does it drop linearly as mag increases? For example, assuming same
aperture two images at magnifications 10x and 20x will have a ratio of
1/2 in brightness?

All assuming visual observations, of course.

Thanks much in advance,
--
I. N. Galidakis
http://users.forthnet.gr/ath/jgal/
------------------------------------------
Eventually, _everything_ is understandable

In message 1093598175.922815@athnrd02, Ioannis
writes
How does brightness/luminosity vary with magnification?

Does it drop linearly as mag increases? For example, assuming same
aperture two images at magnifications 10x and 20x will have a ratio of
1/2 in brightness?

All assuming visual observations, of course.

You get the same answer for photography too. The image gets dimmer with
the square of the magnification factor.

So at 2x magnification the image is twice the linear size and therefore
4x the area - with the same amount of light is spread over that region.

Regards,
--
Martin Brown

Ioannis wrote in message news:1093598175.922815@athnrd02...
How does brightness/luminosity vary with magnification?

When you magnify, you spread the same amount of light over a larger
apparent *area*. Since area has a square relationship with the field
of view, it means that brightness varies inversely with the *square*
of the magnification.

Does it drop linearly as mag increases? For example, assuming same
aperture two images at magnifications 10x and 20x will have a ratio of
1/2 in brightness?

20x will have 1/4 the area, and therefore, 1/4 the brightness of 10x.

All assuming visual observations, of course.

In terms of straight light flux, it doesn't matter.

However, the human element certainly complicates the math. Since i
look through telescopes, i think i have something to say. Since i'm
not an ocular physiologist, i welcome any constructive comments or
corrections.

Our visual perception is non-linear, and decidedly complicated. For
visual deep-sky purposes, you can consider it logarithmic (in English,
we perceive contrasts), with thresholds of detection in brightness and
resolution.

In practical matters, it means:

- Increasing the power increases the visibility of stars. Since
stars cannot be resolved by amateur instruments, their brighness
is not affected by magnification. Magnification dims the
background sky, thus increasing the contrast with the stars. This
can help greatly in resolving star clusters.

- Increasing power allows us to see more detail--to a point. An
object can have plenty of contrast, but if the details aren't big
enough to meet our eye's threshold of resolution, we're not going
to see them.

The ultimate case of this is entire galaxies. In the dark, our
eyes' resolution can be as course as 1/2 degree--the aparent size
of the full Moon! (This is why we cannot read a newspaper article
in the dark, even when we can read the headline.) Most galaxies
are smaller than this, and it shows: With the naked eye, most of
us can see only 4 or 5 of them. The light-gathering aperture of a
telescope is offset by magnification or--at low powers--large exit
pupils, yet we can see many more galaxies through the telescope.

You are probably already familiar with the limitations of
magnification:

- Reduce the surface brightness of an object too much, and we don't
see anything at all, never mind the contrast. Obviously,
increased aperture will offset this.

- Increasing the power beyond tonights atmospheric seeing doesn't
help much. This is usually around 250x - 300x, give or take about
500% (roughly), or thereabouts (approximately). Whether aperture
helps or even hinders here seems to be a matter of one's religion.

- Due to diffraction, aperture imposes a limit on detail that no
amount of magnification can overcome. The general rule of thumb
for maximum *useful* power is about twice the aperture in
millimeters (i.e., about 120x for any telescope that says 525x on
the box), but this varies greatly from person to person.

This is probably more information than you were looking for, but it's
here for you to consider.


Clear skies!

--
------------------- Richard Callwood III --------------------
~ U.S. Virgin Islands ~ USDA zone 11 ~ 18.3N, 64.9W ~
~ eastern Massachusetts ~ USDA zone 6 (1992-95) ~
--------------- http://cac.uvi.edu/staff/rc3/ ---------------

Cousin Ricky wrote:

Ioannis wrote in message news:1093598175.922815@athnrd02...

How does brightness/luminosity vary with magnification?


When you magnify, you spread the same amount of light over a larger
apparent *area*. Since area has a square relationship with the field
of view, it means that brightness varies inversely with the *square*
of the magnification.
[snip]

About half an hour after I posted the question, I thought of it as follows:

The ratio of luminosities, should be proportional to the ratio of the
respective FOV's areas under the different magnifications, since the
amount of light as you say stays the same, which I _believe_ should
reduce to the same answer as yours, since a FOV's area would be
pi*rho^2, (some rho depending on FOV), etc, so the brightness ratios
should be ~(rho_1/rho_2)^2, assuming that double the magnification
halves the radius of the FOV.

Thank you for the extra info, btw

Clear skies!
--
I. N. Galidakis
http://users.forthnet.gr/ath/jgal/
------------------------------------------
Eventually, _everything_ is understandable

I wrote:

[snip]
About half an hour after I posted the question, I thought of it as follows:

The ratio of luminosities, should be proportional to the ratio of the
respective FOV's areas under the different magnifications, since the
amount of light as you say stays the same, which I _believe_ should
reduce to the same answer as yours, since a FOV's area would be
pi*rho^2, (some rho depending on FOV), etc, so the brightness ratios
should be ~(rho_1/rho_2)^2, assuming that double the magnification
halves the radius of the FOV.

Thank you for the extra info, btw

I still have problems calculating the brightness ratio between my two
pairs though, 11x80 and 20x100:

(100/80)^2=1.56, so (keeping magnification constant):

1) Brightness_{100mm lens}=1.56 x Brightness_{80mm lens}

The two sets have different magnifications, so according to what was
said in mine and other posts (keeping lens size constant):

2) x Brightness_{@20x},

where 270'and 140' are the FOVs of the respective pairs,

1) and 2) together, =

Brightness_{100mm x Brightness_{80mm lens@11x}, =

Brightness_{100mm x Brightness_{80mm lens@11x}

Um, but the 20x100 pair is MUCH brighter than the 11x80 pair!

Where's my mistake?

Thanks,

Clear skies!
--
I. N. Galidakis
http://users.forthnet.gr/ath/jgal/
------------------------------------------
Eventually, _everything_ is understandable

Ioannis wrote:
Um, but the 20x100 pair is MUCH brighter than the 11x80 pair!

Where's my mistake?

Greater apparent surface brightness doesn't necessarily equate with
easier to see. First of all, the magnification of binoculars is low
enough that stars appear to be point sources. That means that stars
will appear (100/80)^2 or 25/16 times as bright in the 20x100 as in
the 11x80.

Secondly, even when we're talking about extended objects, many of the
things you see are still small enough that they get easier to see when
they're magnified more, even though the overall image may be dimmer.
That's why some DSOs are better observed at higher magnifications,
even in the same telescope.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

Brian Tung wrote:

Ioannis wrote:

Um, but the 20x100 pair is MUCH brighter than the 11x80 pair!

Where's my mistake?


Greater apparent surface brightness doesn't necessarily equate with
easier to see. First of all, the magnification of binoculars is low
enough that stars appear to be point sources. That means that stars
will appear (100/80)^2 or 25/16 times as bright in the 20x100 as in
the 11x80.

Secondly, even when we're talking about extended objects, many of the
things you see are still small enough that they get easier to see when
they're magnified more, even though the overall image may be dimmer.
That's why some DSOs are better observed at higher magnifications,
even in the same telescope.

Brian,

For stars, I understand what you are saying. But for extended objects
please point out a mistake in my math, as it applies.

The calculations still show that I should see M33, for example, 0.42
times less bright in the 20x100 binos than in the 11x80, whereas in
reality I see it about 2-3 times as bright in the larger pair.

Why the apparent discrepancy?

Brian Tung
--
I. N. Galidakis
http://users.forthnet.gr/ath/jgal/
------------------------------------------
Eventually, _everything_ is understandable

Ioannis wrote:
For stars, I understand what you are saying. But for extended objects
please point out a mistake in my math, as it applies.

I can't. You haven't made one, as far as I can tell. (To be honest,
I only eyeballed your math. It looks right, though.)

The calculations still show that I should see M33, for example, 0.42
times less bright in the 20x100 binos than in the 11x80, whereas in
reality I see it about 2-3 times as bright in the larger pair.

Why the apparent discrepancy?

Because your eye is not a reliable measure of absolute brightness. I
assure you that as long as the optics are reasonable in both, if you
were to take an afocal shot behind the two binoculars, the 20x100 will
have a lower surface brightness (though the image scale is nearly twice
the other). But your eye just doesn't see it that way. It may appear
brighter, for instance, because the sky background is darker in the
20x100.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

Read this!

http://skyandtelescope.com/howto/vis...ticle_78_1.asp

I. N. Galidakis wrote:
The calculations still show that I should see M33, for example, 0.42
times less bright in the 20x100 binos than in the 11x80, whereas in
reality I see it about 2-3 times as bright in the larger pair.

Why the apparent discrepancy?

The 11x80 binoculars produce a 7.3-mm exit pupil. That's pretty large, larger
than most fully dilated 40+ year-old eye pupils. If your eye pupil is, just to
throw out a number, 6.5-mm in size, your binoculars are only operating at 89%
their aperture. That works out to 79% the light-gathering power.

The 20x100 binoculars produce a 5-mm exit pupil. You're almost certainly making
full use of that aperture. Comparing the light-gathering of these with the
11x80 binocs (again, assuming 6.5-mm eye pupils), the 20x100's actually deliver
198% or nearly twice as much light to your eyes.

That, in combination with the lowered threshold contrast of the 100-mm aperture
binoculars and the larger apparent size of M33 in those same binocs, could
easily combine to give the impression that the galaxy looks significantly
brighter even though its surface brightness is actually lower.

Regards,

Bill Ferris
"Cosmic Voyage: The Online Resource for Amateur Astronomers"
URL: http://www.cosmic-voyage.net
=============
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