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Data Reduction of Hartmann Test Ou Yang, Hsien Supervisor : Shiang-yu Wang

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Data Reduction of Hartmann Test Introduction to Hartmann method Hartmann Pattern Data reduction Results & Discussion

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Hartmann method Image quality examination method by detecting wavefront deviation w at certain points. The image aberration can be reconstruct by the data reduction.

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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

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The Hartmann test image Inside focusOutside focusTilted image

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Transverse aberrations for each of the data points on the telescope mirror

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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

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The coefficient of aberration polynomial CoefficientOutside focus Inside focusTilted image A3.585E-143.183E-12-8.457E-13 B4.844E-12-4.493E-11-9.942E-9 C-1.883E-81.025E-65.783E-7 D-7.566E-7-1.342E-11-1.589E-6 E-5.701E-5-3.293E-42.045E-2 F3.464E-4-2.38E-43.148E-4

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The graph of W(x,y) [Outside focus] peak to valley error 11µm

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The graph of W(x,y) [Inside focus] peak to valley error 6.8µm

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The graph of W(x,y) [ Tilted image] peak to valley error 63µm

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The graph of W(x,y) [spherical aberration coefficient] peak to valley error 21µm

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The graph of W(x,y)[coma coefficient] peak to valley error 1.2µm

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The graph of W(x,y)[astigmatism coefficient] peak to valley error 1.3µm

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The graph of W(x,y) [defocusing coefficient] peak to valley error 17µm

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The graph of W(x,y) [tilt about x axis] peak to valley error 5.6µm

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The graph of W(x,y) [tilt about y axis] peak to valley error 3.4µm

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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.

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