[Laser] Re: Fresnel lenses and dispersal angle

[Walt Rauscher]

Sorry, but Spherical aberration is NOT wavelength dependent. That is Chromatic aberration and is due to the refraction angle of the air-substrate (glass, plastic) interface being wavelength dependent and is corrected with multiple elements each with different wavelength dependent refraction not with coatings. 
Most coatings are anti-reflective. This increases the amount of light that passes through the lens which decreases the amount of light lost. Coatings can also be a dielectric interference filter that pass or reflect certain wavelengths.
Spherical aberration is the change in focal length with distance from the center of the lens.
This is why "cheap" telescopes have a high f-number (focal length divided by aperture). I have measured the Spherical aberration of an "Overhead" fresnel lens by making a mask with 1/4 inch holes spaces 1 inch apart from the center to edge. Then by aiming at the sun (infinite object) measured the focal distance of each hole. The results were approximately:
hole at 1in		fl = 9 in
	2in		8.5 in
	3in		7.1 in
	4in		6.25in
	etc.
Note: these are not my actual measures since I do not have my notebook at hand but are representative.
The result is a very large fuzzy area of "best" focus about 2 inch across. To decrease this effect decrease the aperture of the lens. There is also some Chromatic aberration in this lens but it is very minor compared to the Spherical aberration.

All this and a lot more is why most optical equations in basic text books are considered "First order". That is they explain the most significant contribution. Also most have constraints such as "thin lens" or "paraxial rays", "point sources", etc. However these "simplified" equations work well for most of our needs. 

walt rauscher, BSc physics. 

-----Original Message-----
From: laser-bounces at mailman.qth.net
[mailto:laser-bounces at mailman.qth.net]On Behalf Of KY1K
Sent: Thursday, June 16, 2005 1:54 PM
To: Free Space LASER Communications
Subject: Re: [Laser] Re: Fresnel lenses and dispersal angle


Hi Chris,

All ok, except......


>So, to your calculated dispersal, you have to ADD the 'inaccuracy factor', 
>which depends on the quality of your particular lens. I've noticed that 
>early fresnels, such as those in 1960s 'Overhead' transparency projectors 
>are not corrected for spherical aberration, in many cases. This would 
>exacerbate things further.

For those using lasers and LED's, spherical aberration is our friend, not 
an enemy........... The fact a fresnel or an early overhead projector lens 
is NOT corrected makes them desirable, not the other way around.

Spherical aberration is the uniformity of the focal length of the lens as 
the wavelength of the light is varied.

This is used to our benefit, because it is wavelength selective and tends 
to prevent light from undesired wavelengths from reaching the detector. 
Let's say your system is optimized for red. A blue or near IR photon will 
reach the detector in lower quantity because some of the off wavelength's 
will miss the detector due to the variable focal length of the lens for 
these different colors.

If your receiver is only interested in a small portion of the visible 
spectrum, you should strive for optics that are not corrected for spherical 
aberration, not the other way around.

An uncoated glass lens offers no correction for spherical aberration, and 
should be used rather than a coated lens.

Art 


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