Chromatic lens question

[Mkv]

Hello,

A theoretical question. Say I have a large single lens that is not corrected in any way, and produces chromatic aberration (so not a doublet or a triplet, etc). Would it then be possible to take separate pictures with red/green/blue filters with focus adjustments, and then stack them to produce a better image?

[rl]

Theoretically yes, provided the stacking software could cope with the small change in scale factor due to the slightly different focal lengths at different colours.

[Elp]

This is essential what you do with a mono camera. The problem that occurs is because the focus points are slightly different you can get mismatch of star positions when you overlay the data, it's only very very slight. Explaining it easier, one set of data the stars may be spaced out, and one set the stars may be more compressed as if the big bang has happened in reverse, the result you get is a bit like chromatic aberration which is more evident as you go toward the edge of the FOV. You then have to scale you data to get a better overlay.

Edited January 12 by Elp

[vlaiv]

In theory yes. In practice no.

Level of dispersion depends on F/ratio of the lens. Even within single color band - say from 400-500nm representing blue part of spectrum, you will have defocus between different wavelengths. Only single wavelength of light will be in focus at any given time and all the rest will be out of focus.

Trick is to make that out of focus to acceptable level - and that you can do only with very slow telescope. And I don't mean F/10 slow or F/20 slow - I mean very very slow telescope.

See for example this:

https://en.wikipedia.org/wiki/Aerial_telescope

(back in the day refractors used a single lens)

Even faster achromatic doublet lens won't produce nice results using that technique.

[Nik271]

Never mind chromatism - a single spherical lens will have significant spherical aberration at any wavelength (unless it has very large focal ratio).

The solution to this is to create a custom aspherical lens shape, but this can work only in a single wavelength.

There is a good reason astronomy telescope makers moved away from single lenses long ago and did not look back.

[Louis D]

I wonder if you used line filters in the red, green, and blue, could you then get sharper images to be combined into a single RGB image?

I also wonder if you deconvolved the component images in software to reduce the appearance of SA could you then get sharper images?

Certainly, starting with a better image gives better results, but this might make for an interesting challenge to revisit the pre-achromatic era of telescopes and see if modern imaging technology (hardware and software) could improve their images.

[Peter Drew]

Worth a try but I'm not sure if it would work.  In general, achromats are corrected in green so blue and red are usually worse.  I don't know whether it's possible to correct the latter two by using software before adding them together again.  Hope it is!       🙂

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[vlaiv]

2 hours ago, Louis D said:

I wonder if you used line filters in the red, green, and blue, could you then get sharper images to be combined into a single RGB image?

You could use line filters - but that would not produce good looking RGB image.

R, G and B values represent weighted sum over all frequencies. Or to be precise - for sRGB color space, R, G and B components have these color matching functions:

Note that sometimes these color matching functions are below zero in value (which would be physically impossible) - which just means that sRGB color space can't reproduce full gamut of color vision - some colors that exist and we can see - can't be shown on computer screen as they would need to have negative red value (to put it in layman's terms - it would need to be less red than the pure greed on the screen ).

In any case - single lines won't work.

2 hours ago, Louis D said:

I also wonder if you deconvolved the component images in software to reduce the appearance of SA could you then get sharper images?

Unfortunately that won't work either.

I'll explain why.

Spherical aberration and defocus depend on wavelength - in fact they are different for each individual wavelength. Two different stars in the image will produce different spectra and if you weigh aberrations by their spectra (Say one star is bluish and other is red in color - in blue one aberrations that dominate will be from blue side of spectrum while for red one - they will be from red side of spectrum) - you will get different PSF - one that depends on spectrum - which you no longer have as you recorded summed response and not individual wavelengths.

Software has no way of knowing which PSF to apply to which star - and different stars will produce different PSF because of that - so you can't deconvolve with one single PSF - you need to use adaptive - but that adaptive PSF depends on information that you no longer have (spectrum of light).

In principle - you could do following - take singlet lens or achromatic doublet and record Ha or OIII or any other interesting single wavelength (or small bandwidth) - and apply deconvolution as necessary. Since you are recording one wavelength - aberrations will be the same on all stars as it depends on wavelength and there is just one.

That would work - you can produce narrowband image with simple scope like that.

[Louis D]

2 hours ago, vlaiv said:

Spherical aberration and defocus depend on wavelength - in fact they are different for each individual wavelength.

I meant deconvolve the line images.  I guess you could take it further and capture more than just three lines to fill in your graph better.

[davidc135]

How much more evident is sphero-chromatism in, say, an f8 singlet than in an equivalent achromat or apo? Disregarding defocus.

David

[Elp]

If you know what to look for you'll notice it straight away. It's quite easy to see visually during the day when looking at a far off bare tree, images will pick it up easily.

Edited January 13 by Elp

[vlaiv]

2 hours ago, davidc135 said:

How much more evident is sphero-chromatism in, say, an f8 singlet than in an equivalent achromat or apo? Disregarding defocus.

David

No idea.

Never seen either simulated graphs nor the view thru the singlet lens acting as a telescope.

[davidc135]

False colour effects in singlets and achromats would be mostly due to defocus but Vla Sacek in 'Telescope-Optics.net' gives lengthy equations to calculate the SA contributions of both the crown and flint in a doublet example. Varying the wavelength would give an idea of sphero-chromatism.

I'll take a deep breath and see if I can get to grips. The form of a crown lens in a doublet would be far from optimum in a singlet.

David

[davidc135]

Alternatively, I could Ronchi test a singlet in auto-collimation in rgb and see how much of a difference there is.

David