Download Spherical Aberration. q ℓ

Spherical Aberration.
For the pasage through the left side of lens, the two optical paths
q
ℓo = R12 + (so + R1 )2 − 2R1 (so + R1 ) cos φ1
q
ℓ1 = R12 + (s1 − R1 + d)2 + 2R1 (s1 − R1 + d) cos φ1 .
combine to
n1
n2
1
+
=
ℓo
ℓ1
R1
µ
¶
so
s1 + d
−n1 + n2
.
ℓo
ℓ1
We set d = 0 and concentrate on h up the lens where we can approximate
the small angle φ ≃ h/R. we than expand cos φ ∼ 1 − φ2 /2 in the eqns for
1/ℓo ≃1/so − (so + R)h2 /(2s2o R)
1/ℓ1 ≃1/s1 − (s1 − R)h2 /(2s2o R).
The spherical aberration correction to the thin lense formala is
"
ni
n2
1
n1
+
=
(−n1 + n2 ) + h2
so
s1
R1
2so
µ
1
1
+
so
R1
¶2
+
n2
2s1
µ
1
1
−
R1
s1
¶2 #
.
This extra positive term causes the ray in the lens to bend down passing
before the focus, This is called a longitudinal spherical aberration.
URL on lens aberrations:
¡ a href=”http://www.photonics.com/EDU/Handbook.aspx?AID=25443”¿Example
of lens aberations¡/a¿ (with ways to avoid defects in imagery)
¡ a href=”http://www.edmundoptics.com/technical-resources-center/optics/compar
of-optical-aberrations/”¿Edmunds Optical webpage¡/a¿
¡ a href=”https://en.wikipedia.org/wiki/Optical aberration”¿WikiPedia
articles aware of its weakness as first two are not.¡/a¿
¡ a href=”https://micro.magnet.fsu.edu/primer/java/aberrations/spherical/index.ht
microscope optical aberations¡/a¿ Its itemst starts in different order:
field curvature. (java tutorials) astigmatism; chromatic aberration;
comatic aberration; curvature of field; geometric distortion; spherical
aberration; focus depth and spherical aberration; cover glass thickness
correction; adjustment of objective correction collars;
¡ a href=”https://micro.magnet.fsu.edu/primer/lightandcolor/opticalaberrations.ht
defects in lens systems (aimed at optical microscope with java tutorials¿¡/a¿