data reduction of hartmann test ou yang, hsien supervisor : shiang-yu wang
TRANSCRIPT
Data Reduction of Hartmann Test
歐陽嫻 Ou Yang , HsienSupervisor : Shiang-yu Wang
Data Reduction of Hartmann Test
• Introduction to Hartmann method
• Hartmann Pattern
• Data reduction
• Results & Discussion
Hartmann method• Image quality examination method by detectin
g wavefront deviation w at certain points.
• The image aberration can be reconstruct by the data reduction.
d
y
y
w
d
x
x
w
;
Hartmann pattern• diameter of the hole : 1cm
• distance between two holes : 4 cm
• # of holes : 140
The mask was installed in front of the secondary mirror of the TAOS#1 telescope
The Hartmann test image
Inside focusOutside focus Tilted image
Transverse aberrations for each of the data points on the telescope mirror
Outside focus
-400
-300
-200
-100
0
100
200
300
400
-400 -200 0 200 400
x(pixel)
y(pi
xel) Theoretical position
Measured position
Transverse aberrations for each of the data points on the telescope mirror
Inside focus
-80
-60
-40
-20
0
20
40
60
80
-100 -50 0 50 100
x(pixel)
y(pi
xel)
Theoretical position
Measured poition
Transverse aberrations for each of the data points on the telescope mirror
Tilted image
-80
-60
-40
-20
0
20
40
60
80
-80 -30 20 70
x(pixel)
y(pi
xel) Theoretical position
Measured position
Aberration Polynomial for Primary Aberration
where
– A = spherical aberration coefficient– B = coma coefficient– C = astigmatism coefficient– D = defocusing coefficient– E = tile about x axis– F = tile about y axis
FxEyDCByAyxW yxyxyxyx
2222222
322,
The coefficient of aberration polynomial
Coefficient Outside focus Inside focus Tilted image
A 3.585E-14 3.183E-12 -8.457E-13
B 4.844E-12 -4.493E-11 -9.942E-9
C -1.883E-8 1.025E-6 5.783E-7
D -7.566E-7 -1.342E-11 -1.589E-6
E -5.701E-5 -3.293E-4 2.045E-2
F 3.464E-4 -2.38E-4 3.148E-4
The graph of W(x,y) [Outside focus]peak to valley error 11µm
The graph of W(x,y) [Inside focus]peak to valley error 6.8µm
The graph of W(x,y) [ Tilted image]peak to valley error 63µm
The graph of W(x,y) [spherical aberration coefficient]peak to valley error 21µm
The graph of W(x,y)[coma coefficient]peak to valley error 1.2µm
The graph of W(x,y)[astigmatism coefficient]
peak to valley error 1.3µm
The graph of W(x,y) [defocusing coefficient]
peak to valley error 17µm
The graph of W(x,y) [tilt about x axis]
peak to valley error 5.6µm
The graph of W(x,y) [tilt about y axis]
peak to valley error 3.4µm
summary
• The aberration of the optical system can be obtained by the hartmann test.
• The hartmann test can help the alignment sequence of optical systems.
• More detailed aberration terms can be obtained by the same procedure.