V Curves, how good is good?

[Bill McLaughlin]

Tried to find this with a search but if it is there, I cannot find it.

I have been using FocusMax since it was announced at the old "Imaging the Sky" conference years ago and generally like it.

I have always wondered why the slopes have six digits after the decimal. I would have to assume that this is a pretty high degree of what a machinist would call "false precision". That is, some of the digits to the right just don't matter much.

The question is, just how many digits should one actually pay attention to? I would assume this would also depend on F ratio to a degree as the focal band is narrower with faster systems.

Mainly I would like to be able to compare V curves taken with different filters. They are always different to a small degree, even with supposedly parfocal filters and even with many data points, clean curves, low PIDs, etc.

So at what point (decimal-wise) does a different final curve indicate a truly different curve and different focal situation?

For example, for situations I KNOW are different:

No Filter (not clear, none):

RightSlope =0.051096
LeftSlope =-0.051099

Red Filter:

RightSlope =0.051747
LeftSlope =-0.051742


So here, with clearly different situations, where clearly different curves would be needed, the
differences show up at the fourth decimal.

How about the 5th decimal, is that significant as well?

Thanks

[John Winfield]

Hi Bill,

Different filters should not affect the v-curve, they only cause an offset to the final focus position.
You can use a single v-curve to cover all the filters on a given setup.

Cheers,

John

[Bill McLaughlin]

Theory says yes. That has not been my (since FocusMax was released) real world experience. If theory is right, then why then am I getting repeatably different curves for different filters? They are quality filters, first the SBIG filters and then Don's version one and now his version two....

In any case, the same question remains even if the theory is right and my data is wrong. Which digit is the last significant one?

[Bill McLaughlin]

Data:

All at least 10 curves with 64 points each. All during decent seeing and with high PID data not used (tossed out, not one of the 10 component curves).

No Filter:

RightSlope =0.051096
LeftSlope =-0.051099

Red Filter:

RightSlope =0.051747
LeftSlope =-0.051742

Lum Filter:

RightSlope =0.051406
LeftSlope =-0.051386

Green Filter:

RightSlope =0.051929
LeftSlope =-0.051945

Blue Filter:

RightSlope =0.051774
LeftSlope =-0.051788

Ha Filter:

RightSlope =0.051476
LeftSlope =-0.051460


If the theory is right and "all curves with the same mirrors/lenses are the same", then the 5th digit has to be just noise as they are widely different. But if THAT is the case then why are the right and left slopes the same to the 5th digit in nearly every case?

BTW, this is a 14.5 inch f9 RCOS with an AOL/SBIG 11000M. AOL was, of course, not operating during the curve gathering. It does have one refractive element other than the AOL and that is the RCOS flattener.

If one were to ask my theory, I would say that the flattener is not quite perfectly apochromatic.

Which leads back to the original question - what digit is significant?

[John Winfield]

What was the variability of the 10 curves you took for each filter - those data should give you your answer, no?

John

[Dick Berg]

Hi Bill,

Interesting data, and very good data I have to say. It's somewhat of a misnomer to say right and left slopes, because what you are really measuring is the "slope" in front of the focus point and behind the focus point.

I think of it like this. Imagine the light cone from the objective coming down the tube toward the back, converging to a point at the focus (well, obviously some fuzziness there...). What FocusMax is doing is essentially measuring the apex angle, or slope, of that cone. First the slope of the cone in front of the focus (if you have FMx set to start inside the focus) and then the slope of the cone outside of focus. In a perfect world of perfect measurement, these two slope values will be identical.

Your right and left slopes are practically identical - don't complain!! Theoretically, if the two surfaces of a filter are parallel, then the shape (angle; slope) of that converging cone will not change. If the thickness of the filters differ, then the focal point will be offset when compared one from another. This is why one pays so much for "parfocal" filters.

So John's right - unless the front and back surface of the filters are not made properly (and thus wedge-shaped), there will only be just a numerical statistical difference between the slopes for the various filters. I think you could average them all together and be happy.

[John Winfield]

Dick,

I think the point Bill makes about his system not being par-focal for different wavelengths is quite key - if the focal length is different for different filtered wavelengths, then the focal ratio will also be different and thus the slope.

So, the theory stating that the thickness of the filter doesn't matter is true, but the non-convergence of the different wavelength light is a different matter.

John

[John Winfield]

Still, having said that, I'd imagine the effect of that slope delta will be lost in the noise of measuring best focus in seeing effects.

I'd suggest averaging them out and using that

John

[Bill McLaughlin]

I think the point Bill makes about his system not being par-focal for different wavelengths is quite key - if the focal length is different for different filtered wavelengths, then the focal ratio will also be different and thus the slope.

So, the theory stating that the thickness of the filter doesn't matter is true, but the non-convergence of the different wavelength light is a different matter.

Still, having said that, I'd imagine the effect of that slope delta will be lost in the noise of measuring best focus in seeing effects.

I'd suggest averaging them out and using that

The interesting thing here is that this system is one that is essentially identical (except for aperture, which varies with the user) to that being used by many if not most of the top imagers for long focal length use. I have never seen or heard anyone mention or discuss this issue despite having used such systems (OGS then RCOS) for over 10 years. It seems to be pretty much ignored. That may indeed be because the curves generally gathered and used may be "good enough" given the other variables such as tracking, seeing, etc.

Having said that, the quest in this hobby is a quest for excellence and perfection so the question remains. Where, exactly is the significant (FocuseMax) digit when it comes to what is or is not usable for perfect focus with a given configuration? This seems to be a pretty important piece of information that is seemingly either unknown or at least not well known. The reason for oddness in the numbers can be debated and could have numerous causes, but it seems to me still important to be able to look at a good set of curves and say "curve A is effectively the same as curve B" or "I guess they are different enough to use a different curve for the different filter/lens, configuration, etc."

It should be possible to calculate if one knows the workings of Focusmax and the step size at the focal plane of the system (easy to find out) since the depth of focus of an F9 system is (rough number) about .009 inch. If a curve was enough different from the "ideal for that configuration" curve that using that "non-ideal" curve might put one outside that range this would be, it seems to me, cause to use a more appropriate curve. While it may well be that under most seeing conditions one would never see the difference, I would hate to think that I was missing a few tenths of an arcsec when the seeing gives me one of those all-too-rare perfect nights!

In fact, I have seen a couple nights here at home recently with raw 800 second exposure FWHM in a few images as low as 1.7 arcsec. Could that have "really" been 1.6 or 1.5?

That is the problem. The better it gets, the more one wonders if one could do just a bit better....

[John Winfield]

Hi Bill,

There's no secret sauce to the fmax internals - the v-curve slopes are just that - the slope of the plot of hfd v's focuser position.

Given that, it's a simple piece of math to calculate the error introduced to the best focus position given a defined error in the slope measurement and a given starting hfd.

John