[ATM] additional lurie-houghton degrees of freedom

[vladimir sacek]

 Guy Brandenburg wrote:

>I was just doing some playing around with OSLO and >my 8" f/5 
>Lurie-Houghton design. I found that you have >to keep surface # 1 and 
>surface #2 very, very close to >each other; if they are one inch apart, the 
>spot diagrams >go downhill pretty fast. But if R2 and R4 are as much as >5 
>inches different, there seems to be essentiall no change >in the spot 
>diagrams AFAICT.

The two lens elements of the Houghton corrector
need to have near identical power (f.l.) of opposite
signs in order to keep secondary spectrum near cancelled.
Any changes in the radii that causes increase in the power
disparity between the two elements will increase secondary
spectrum. And if the change in  radii result in a nearly
similar change in power for the two elements, the amount
of secondary spectrum also won't change appreciably.

Similarly, the sum of spherical aberration of the two
elements needs to nearly cancel that of the mirror. The
most significant element determining the amount of
aberration of the single lens element is its focal length
(the aberration changes with the third power of it).
If the radii change causes the two element powers to go
in opposite directions, the effect will bi much more obvious
than in the scenario where it causes both elements power
change in the same direction (sign), and in the similar amount
(this applies to spherochromatism as well).

Interestingly, the R/V raytrace gives less than optimum s.a.
correction for the design (about 1/5 wave over-correction).
Their T-design gives zero s.a. radii (absolute values) as
R1,3=67.42" and R2,4=175.96" (which agrees with the
 formulae: http://www.telescope-optics.net/Houghton.htm ).
Lens thickness is about half of yours (probably too thin),
but it doesn't affect spherical correction.

Btw, if the corrector radius is 3.75", isn't it a 7.5" f/5.3 system?

Vlad