Infinity focus point

[Andrew*]

Is there any formula to work out how distant an object needs to be to focus at the same point as infinity?

With short f/l camera lenses, for example, this is usually less than 50m, but I've no idea with long f/l telescopes.

Andrew

[Merlin66]

Andrew,

The "normal" depth of field for a photographic application is described in this excellent article:

Depth of field

Does this help?

For focus tolerance with a telescope, which is slightly different the formula to give a "circle of confusion" 1/4 wave limit is:

f= 4 x Lamda x F^2

where f is the allowable focus tolerance(mm)

Lamda the wavelength (green=550nm)

F the focal ratio

So, for a f5 system in green light we need to focus within 0.055mm!!!

[Andrew*]

Hi Ken,

Just worked it out, sorry!

Hyperfocal distance - Wikipedia, the free encyclopedia

By my calculation based on a 0.03mm CoC:

80mm f/5 scope, the minimum distance is 1.1km

120mm f/7.5 scope, 3.6km

16" f/4.5 scope, 25km

14" f/10 scope, 40km

Actually much further than I expected, but it might be a bit harsh for the CoC - that's a typical CoC for 35mm film, but I'm mainly thinking of visual, which can compensate a bit...

Andrew

[BlueAstra]

I've noticed that with my C8 SCT the focus position for a pylon about 1km away is not the same position as used for the moon, which is also not the same position for stars.

[beamish]

Andrew , how did you come to determine your CoC ??

[Rossco72]

Recent observations of our moon and Jupiter have identified ever so slight focus shift at f7 (85mm)

[Andrew*]

But the moon is thousands of km away! Surely there can't be a focus change of more than a few thousandths of a mm?

Andrew , how did you come to determine your CoC ??

I just used the standard 35mm film value of 0.03. It might only need to be 0.1mm for visual use, which would obviously lower these distances to 0.3 the current values.

Andrew

[Merlin66]

Andrew,

The COC for visual should be the size of the Airy Disk, hence the 1/4 wave tolerance on the focuser formula.

Airy Disk diameter=2.44 x lamda x F/D micron

So a 200mm f8 scope would give a disk of 11 micron; a 400mm f4 would be 5.5 micron....much less than the figures you've used.

Ken

[brianb]

the focus position for a pylon about 1km away is not the same position as used for the moon, which is also not the same position for stars.

Something not right there. The correct focus for all astro objects (even earth satellites) is the same for all scopes up to several metres aperture ... the focus of the eye does however vary a bit with the brightness of the object.

[Andrew*]

Ah, okay. I was just going by my experience with imaging, where it just needs a tiny tweak to take it off perfect focus, but it's so much easier with visual because your eyes can adjust the last bit of focus.

But if we go with the Airy disc size, which is a much more accurate way of looking at the problem, my values increase somewhat:

80mm f/5 is 4.8km

120mm f/7.5 is 10.7km

16" f/4.5 is 123.1km

At least I think that's right if I've understood your formula right- is F/D the focal ratio?

Andrew

[Merlin66]

Yes, F/D is the focal ratio of the system.

Remember this formula gives the LINEAR size of the Airy disk.

Visual....is something else again;)

[Andrew*]

So my working for the 80mm f/5 was:

Airy disc = 2.44*0.00055*5 = 0.00671mm

Hyperfocal point = 400^2/(5*0.00671) = 4.8km

[Andrew*]

Do continue!

[Merlin66]

The visual Airy disk diameter is:

Sine Theta = 2.44 x lamda/D

for small angles:

sine Theta = Theta (radians)

So the apparent size of the Airy Disk varies with the diameter (D) of the objective...as you would expect.

BUT the intensity distribution of this disk is a Gaussian curve, and the FWHM (Full Width Half Max) determines the Rayleigh resolution.

(Like the Dawes Limit...but when the two FWHM image disks just touch, then they are resolved).

When we talk about star images being 3" arc (or seeing conditions etc) we are really talking about FWHM sizes.

So what do you use for the COC???

The perceived FWHM or the actual Airy Disk size??

This is where the formula for Critical focus tolerance in the earlier post comes in....we can't always tell the difference in precise focus position ie on an f10 scope we can move the focus 0.22mm before loosing the Airy Disk (1/4 wave tolerance) whereas on a f4 system we only have 0.035mm tolerance. Very, very, difficult to get absolute accurate focus on a f4 telescope.

When imaging, use the FWHM monitoring function (which most imaging programs can show) to determine best focus.

I thinks that's enough for one day:o

Ken