### Comparing Versions of Diverger lens Residual Spherical aberration

Thin lens diverger SA contribution is given by C8 the amplitude of the zernike polynomial Z8 (Wyant enummeration)

C8 = (1/3072)*(f/(F#^4))*[(n/(n-1))^2 + (n+2)/(n*(n-1)^2)*[B + 2*((n^2-1)/n*(n-1)^2)*C]^2 - (n/(n+2))*C^2]

where

B is the Coddington shape factor of the lens (0 for an equibiconvex lens, -1 for light incident on the plane face of a PCX lens, +1 for light incident on the convex face of a PCX lens)

C is The Coddington Conjugate variable (0 for equal image and object conjugates, -1 for the object at infinity, +1 for the object at the front focus)

f is the focal length of the lens

F# is the test beam F#

Raytrace results:

SA contribution of a EBCX Diverger Lens

Example 1:

10mm EFL BK7 EBCX diverger lens used to test a 25" F/2.5 mirror at its CoC

the difference in C8 between the test and reference beams = 1.2nm.

This primarily due the diverger lens operating with an effective source at the focus (62.5" from the lens) of the test mirror for the reference beam

whereas for the test beam the source distance is at infinity.

Example 2:

10mm EFL BK7 EBCX diverger lens used to test a 16" F/2.5 mirror at its CoC

the difference in C8 between the test and reference beams = 1.8nm.

This primarily due the diverger lens operating with an effective source at the focus (40" from the lens) of the test mirror for the reference beam

whereas for the test beam the source distance is at infinity.

Example 3:

10mm EFL BK7 EBCX diverger lens used to test a 8" F/8 mirror at its CoC

the difference in C8 between the test and reference beams = 0.34nm.

This primarily due the diverger lens operating with an effective source at the focus (62.5" from the lens) of the test mirror for the reference beam

whereas for the test beam the source distance is at infinity.

Example 4:

10mm EFL BK7 EBCX diverger lens used to test a 6" F/15 mirror at its CoC

the difference in C8 between the test and reference beams = 0.018nm.

This primarily due the diverger lens operating with an effective source at the focus (62.5" from the lens) of the test mirror for the reference beam

whereas for the test beam the source distance is at infinity.

Example 5:

6mm EFL N-SF5 EBCX diverger lens used to test a 28" F/2.5 mirror at its CoC

the difference in C8 between the test and reference beams = 0.246nm.

This primarily due the diverger lens operating with an effective source at the focus (70" from the lens) of the test mirror for the reference beam

whereas for the test beam the source distance is at infinity.

Example 6:

6mm EFL N-SF5 EBCX diverger lens used to test a 20" F/3 mirror at its CoC

the difference in C8 between the test and reference beams = 0.138nm.

This primarily due the diverger lens operating with an effective source at the focus (60" from the lens) of the test mirror for the reference beam

whereas for the test beam the source distance is at infinity.

Example 7:

6mm EFL N-SF5 EBCX diverger lens used to test an 11" F/2.5 mirror at its CoC

the difference in C8 between the test and reference beams = 0.633nm.

This primarily due the diverger lens operating with an effective source at the focus (27.5" from the lens) of the test mirror for the reference beam

whereas for the test beam the source distance is at infinity.

SA contribution of a PCX Diverger lens

|Delta(C8)| = (1/1536)*(f/(F#^4))*[(n+2)/(n*(n-1)^2]

Where the sign of Delta(C8) = C8(Test) - C8(Reference) depends on the orientation of the PCX lens.

= - when the plano side of the PCX lens faces the collimated test beam

= + when the convex surface of the PCX lens faces the collimated test beam

Example 1:

10mm EFL BK7 PCX diverger lens used to test a 6" F/15 mirror at its CoC

the difference in C8 between the test and reference beams = 1.9nm.

This primarily due the asymmetric shape of the diverger lens.

Example 2:

10mm EFL BK7 PCX diverger lens used to test a 16" F/2.5 mirror at its CoC

the difference in C8 between the test and reference beams = 125nm.

This primarily due the asymmetric shape of the diverger lens.

Example 3:

10mm EFL BK7 PCX diverger lens used to test an 8" F/8 mirror at its CoC

the difference in C8 between the test and reference beams = 21nm.

This primarily due the asymmetric shape of the diverger lens.

Example 4:

10mm EFL BK7 PCX diverger lens used to test a 6" F/15 mirror at its CoC

the difference in C8 between the test and reference beams = 1.7nm.

This primarily due the asymmetric shape of the diverger lens.