Thought maybe I would chime in on this subject. I think you need to consider many things in Yuri's comment. ...

That's some good context Richard!

So true. There's more to observing than just a brochure.

Started by
mgwhittle
, Nov 19 2013 02:12 PM

327 replies to this topic

Posted 25 January 2015 - 01:01 PM

Thought maybe I would chime in on this subject. I think you need to consider many things in Yuri's comment. ...

That's some good context Richard!

So true. There's more to observing than just a brochure.

- Ziggy943 likes this

Posted 25 January 2015 - 10:10 PM

There's probably a formula you can use to predict how much larger an obstructed scope needs to be to match a smaller unobstructed one in contrast transfer. Ed Moreno loves contrast transfer graphs. I bet he could generate a table showing the aperture equivalency of refractor vs. SCT vs. Dob/Newt contrast transfer. Now that would be informative, even if based on stated assumptions of equivalent figure quality for all instruments.

Jim, assumption of even optical quality is the easy part. The effect of central obstruction is probably the only subject in my fairly long encounter with telescope optics that have obvious theoretical inconsistencies. For one, the standard model tells us that central obstruction in any size (within the range normally found in telescopes) does not affect MTF cutoff frequency (i.e. that its resolution threshold vs. that of comparable unobstructed aperture doesn't change). I don't think we need calculation of any type to conclude that if the central maxima gets smaller due to the presence of central obstruction, and the resulting PSF becomes nearly identical to that of somewhat larger aperture aberrated by a relatively modest amount of spherical aberration, the two apertures will also have nearly identical MTF cutoff frequency. On the theoretical level, that is also supported by the PSF and MTF being Fourier pair, where the width (frequency range) od the MTF is directly (inversely) proportional to the angular size of the diffraction maxima. That directly contradicts the standard MTF c.obstruction model, whose formalism is based on the aperture diameter, and as such does not - and cannot - account for the change in central maxima size.

As an example, let's look at a 32% linear obstruction. It causes central maxima to shrink by nearly 10%, and the PSF becomes nearly identical to that of 10% larger (linearly) aperture aberrated by 1/4 wave p-v of spherical aberration (that assuming coherent point source, which is not a correct assumption for the field condition most of the time, but will come to that after this).

**co.PNG** **31.69KB**
25 downloads

Note that these plots are done in polychromatic light (440-680nm). If OSLO output is correct - and there is no reason at this point to doubt that - the reduction of central maxima due to the central obstruction is even greater in polychromatic light (10% figure is for monochromatic light). Consequently, it is still some 7% smaller than that in the 10% larger aberrated aperture, and contrast transfer is somewhat better than its toward high frequencies. Obviously, what seems to be the actual effect (it is the actual effect with the PSF,hence there is no physical basis not to be with MTF as well) is significantly different than that predicted by the standard MTF model. Contrast drop in a better part of the left side of MTF graph is comparable to that of nearly 20% smaller aperture, not 32% smaller as implied by the standard model. Bright low-contrast (planetary) detail resolution threshold is only about 7% smaller, and the cuttof frequency is increased by some 15% (only 10% on the plot, which is based on the initial assumption of 10% reduction in the size of central maxima).

But even this may not be correct. The standard PSF model assumes coherent (monochromatic) point source, while we are normally dealing with polychromatic light. The difference is that the former is for all practical purposes coherent light, and the latter closer to incoherent. The former is linear in amplitude and quadratic in intensity, while th latter is quadratic in amplitude and linear in intensity. In other words, due to the phase of individual waves with coherent light being tightly correlated, they add up in the amplitude first, and then are squared for the intensity.

On the other hand, the phase-uncorrelated waves of incoherent light have their individual amplitudes squared for (individual) intensity first, and then add up directly as intensities. So, while doubling the flux will quadruple the intensity with coherent light, it will only double it with incoherent light (in terms of aperture, doubling its diameter will increase intensity 16-fold with coherent light, while only 4-fold with incoherent).

The implication for the effect of central obstruction is that with incoherent light it won't take out - i.e transfer out from central maxima - nearly 20% of energy with 32% obstruction, but only about half as much. So its actual actual effect would've been even smaller than what above plot indicates.

Was this helpful at all?

Vla

**Edited by wh48gs, 27 January 2015 - 07:17 AM.**

Posted 25 January 2015 - 10:14 PM

There's probably a formula you can use to predict how much larger an obstructed scope needs to be to match a smaller unobstructed one in contrast transfer. Ed Moreno loves contrast transfer graphs. I bet he could generate a table showing the aperture equivalency of refractor vs. SCT vs. Dob/Newt contrast transfer. Now that would be informative, even if based on stated assumptions of equivalent figure quality for all instruments.

Jim, assumption of even optical quality is the easy part. The effect of central obstruction is probably the only subject in my fairly long encounter with telescope optics that have obvious theoretical inconsistencies. For one, the standard model tells us that central obstruction in any size (within the range normally found in telescopes) does not affect MTF cutoff frequency (i.e. that its resolution threshold vs. that of comparable unobstructed aperture doesn't change). I don't think we need calculation of any type to conclude that if the central maxima gets smaller due to the presence of central obstruction, and the resulting PSF becomes nearly identical to that of somewhat larger aperture aberrated by a relatively modest amount of spherical aberration, the two apertures will also have nearly identical MTF cutoff frequency. On the theoretical level, that is also supported by the PSF and MTF being Fourier pair, where the width (frequency range) od the MTF is directly proportional to the angular size of the diffraction maxima. That directly contradicts the standard MTF c.obstruction model, whose formalism is based on the aperture diameter, and as such does not - and cannot - account for the change in central maxima size.

As an example, let's look at a 32% linear obstruction. It causes central maxima to shrink by nearly 10%, and the PSF becomes nearly identical to that of 10% larger (linearly) aperture aberrated by 1/4 wave p-v of spherical aberration (that assuming coherent point source, which is not a correct assumption for the field condition most of the time, but will come to that after this).

Note that these plots are done in polychromatic light (440-680nm). If OSLO output is correct - and there is no reason at this point to doubt that - the reduction of central maxima due to the central obstruction is even greater in polychromatic light (10% figure is for monochromatic light). Consequently, it is still some 7% smaller than that in the 10% larger aberrated aperture, and contrast transfer is somewhat better than its toward high frequencies. Obviously, what seems to be the actual effect (it is the actual effect with the PSF,hence there is no physical basis not to be with MTF as well) is significantly different than that predicted by the standard MTF model. Contrast drop in a better part of the left side of MTF graph is comparable to that of nearly 20% smaller aperture, not 32% smaller as implied by the standard model. Bright low-contrast (planetary) detail resolution threshold is only about 7% smaller, and the cuttof frequency is increased by some 15% (only 10% on the plot, which is based on the initial assumption of 10% reduction in the size of central maxima).

But even this may not be correct. The standard PSF model assumes coherent (monochromatic) point source, while we are normally dealing with polychromatic light. The difference is that the former is for all practical purposes coherent light, and the latter closer to incoherent. The former is linear in amplitude and quadratic in intensity, while th latter is quadratic in amplitude and linear in intensity. In other words, due to the phase of individual waves with coherent light being tightly correlated, they add up in the amplitude first, and then are squared for the intensity.

On the other hand, the phase-uncorrelated waves of incoherent light have their individual amplitudes squared for (individual) intensity first, and then add up directly as intensities. So, while doubling the flux will quadruple the intensity with coherent light, it will only double it with coherent light (in terms of aperture, doubling its diameter will increase intensity 16-fold with coherent light, while only 4-fold with incoherent).

The implication for the effect of central obstruction is that with incoherent light it won't take out - i.e transfer out from central maxima - nearly 20% of energy with 32% obstruction, but only about half as much. So its actual actual effect would've been even smaller than what above plot indicates.

Was this helpful at all?

Vla

Yes, thanks, as always, Vla.

- Jim

Cloudy Nights LLC Cloudy Nights Sponsor: Astronomics |