George Smith, Raymond A. Applegate, and David A. Atchison, "Assessment of the accuracy of the crossed-cylinder aberroscope technique," J. Opt. Soc. Am. A 15, 2477-2487 (1998)
Simulations of the optics of the Howland crossed-cylinder aberroscope technique show that errors in alignment, data collection, and analysis can lead to unexpected asymmetries of the determined aberrations in a rotationally symmetric system. In particular, coma can be incorrectly indicated. The magnitude of the error in aberration measurement depends on the magnitude of the alignment, data collection, and alignment errors. These findings indicate that the tolerances for setting up the technique and data collection should be analyzed thoroughly before quantitative significance is given to the determined aberration coefficients.
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Comparison of the Expected and Centered Crossed-Cylinder Aberration Coefficient Values and Actual Values for Various Sources of Error in the Setupa
Error Source
Expected
Centered Crossed Cylinder
Rotation by +5°
Decentration (+1 mm upward)
Both Together
Crossed Cylinder Alone
Grid Alone
Both Together
Crossed Cylinder Alone
Grid Alone
Displacement
0
0
0
0
0
-0.012838
5.019549
-5.002464
0
0
0
0
0
0.085822
0.004052
0.086693
Astigmatism
0.424023
0.418905
0.631255
0.851041
0.192814
0.469576
0.425330
0.475335
-5.139676
-5.156068
-5.137875
-5.086516
-5.138391
-5.159043
-5.166674
-5.110737
0.203598
-0.024534
0.642753
0.568302
0.421747
0.570839
Comalike terms
0
0
0
0
0
0.002312
-0.019334
0.021626
0
0
0
0
0
0.102197
-0.002978
0.104862
0
0
0
0
0
0.011642
-0.004058
0.030541
0
0
0
0
0
0.102930
-0.000872
0.103495
Spherical-aberration-like terms
0.024071
0.025235
0.025256
0.023516
0.026958
0.025397
0.025324
0.025336
0
0.004696
-0.006581
-0.005925
0.003005
0.004320
0.004719
0.004533
0.048142
0.050668
0.050490
0.050582
0.050768
0.051535
0.050811
0.051363
0
0.015939
0.014285
0.005224
0.004588
0.004694
0.004711
0.024071
0.025036
0.027036
0.023463
0.026096
0.025293
0.026001
Grid size (on retina)
0.083416
0.083296
0.083273
0.083141
0.083209
0.083128
0.083128
0.083296
All results are for a undistorted grid, with a 1-mm grid spacing, placed 30 mm from the anterior corneal surface of the eye.
Table 6
Comparison of the Expected and Centered Crossed-Cylinder Aberration Coefficient Values and Actual Values for Various Sources of Error in the Data Collection and Analysisa
All results are for a undistorted grid, with a 1-mm grid spacing, placed 30 mm from the anterior corneal surface of the eye.
By one grid element upward.
Table 7
Effect of Uncertainty on Reading the Grid Points, Assuming That the Uncertainty on Each Grid Point Is Defined by a Uniform Probability Distribution with Extreme Values Being the Width of a Grid Elementa
The means and standard deviations were calculated from 50 repeated simulations. The aberrations were calculated for a point 1° off axis.
Standard deviation.
Table 8
Comparison of the Expected and Centered Crossed-Cylinder Aberration Coefficient Values and Actual Values for Various Sources of Error in the Data Collection and Analysisa
Error Source
Expected
Centered Crossed Cylinder
Subgrid (3, 3) to (7, 7)
Subgrid (4, 4) to (7, 7)
Displacement
0
0
0.018897
-0.033052
0
0
Astigmatism
0.424023
0.421954
0.421961
0.389221
-5.139676
-5.147680
-5.155507
-5.366720
Comalike terms
0
0
-0.002164
-0.012411
0
0
-0.005883
-0.036358
0
0
0
0
Spherical-aberration-like terms
0.024071
0.025429
0.025068
0.024914
0
0.003675
0.003480
0.001006
0.048142
0.050568
0.048516
0.045002
0
0.024071
Grid size
0.083416
0.083296
0.083296
0.081375
All results are for a undistorted grid, with a 1-mm grid spacing, placed 30 mm from the anterior corneal surface of the eye. The subgrid values were the same as those for a whole grid with the corresponding weights set to zero.
Tables (8)
Table 1
Important Symbols Used in Equations
Distance from the cross cylinder to eye pupil (vertex distance +3.0 mm)
Comparison of the Expected and Centered Crossed-Cylinder Aberration Coefficient Values and Actual Values for Various Sources of Error in the Setupa
Error Source
Expected
Centered Crossed Cylinder
Rotation by +5°
Decentration (+1 mm upward)
Both Together
Crossed Cylinder Alone
Grid Alone
Both Together
Crossed Cylinder Alone
Grid Alone
Displacement
0
0
0
0
0
-0.012838
5.019549
-5.002464
0
0
0
0
0
0.085822
0.004052
0.086693
Astigmatism
0.424023
0.418905
0.631255
0.851041
0.192814
0.469576
0.425330
0.475335
-5.139676
-5.156068
-5.137875
-5.086516
-5.138391
-5.159043
-5.166674
-5.110737
0.203598
-0.024534
0.642753
0.568302
0.421747
0.570839
Comalike terms
0
0
0
0
0
0.002312
-0.019334
0.021626
0
0
0
0
0
0.102197
-0.002978
0.104862
0
0
0
0
0
0.011642
-0.004058
0.030541
0
0
0
0
0
0.102930
-0.000872
0.103495
Spherical-aberration-like terms
0.024071
0.025235
0.025256
0.023516
0.026958
0.025397
0.025324
0.025336
0
0.004696
-0.006581
-0.005925
0.003005
0.004320
0.004719
0.004533
0.048142
0.050668
0.050490
0.050582
0.050768
0.051535
0.050811
0.051363
0
0.015939
0.014285
0.005224
0.004588
0.004694
0.004711
0.024071
0.025036
0.027036
0.023463
0.026096
0.025293
0.026001
Grid size (on retina)
0.083416
0.083296
0.083273
0.083141
0.083209
0.083128
0.083128
0.083296
All results are for a undistorted grid, with a 1-mm grid spacing, placed 30 mm from the anterior corneal surface of the eye.
Table 6
Comparison of the Expected and Centered Crossed-Cylinder Aberration Coefficient Values and Actual Values for Various Sources of Error in the Data Collection and Analysisa
All results are for a undistorted grid, with a 1-mm grid spacing, placed 30 mm from the anterior corneal surface of the eye.
By one grid element upward.
Table 7
Effect of Uncertainty on Reading the Grid Points, Assuming That the Uncertainty on Each Grid Point Is Defined by a Uniform Probability Distribution with Extreme Values Being the Width of a Grid Elementa
The means and standard deviations were calculated from 50 repeated simulations. The aberrations were calculated for a point 1° off axis.
Standard deviation.
Table 8
Comparison of the Expected and Centered Crossed-Cylinder Aberration Coefficient Values and Actual Values for Various Sources of Error in the Data Collection and Analysisa
Error Source
Expected
Centered Crossed Cylinder
Subgrid (3, 3) to (7, 7)
Subgrid (4, 4) to (7, 7)
Displacement
0
0
0.018897
-0.033052
0
0
Astigmatism
0.424023
0.421954
0.421961
0.389221
-5.139676
-5.147680
-5.155507
-5.366720
Comalike terms
0
0
-0.002164
-0.012411
0
0
-0.005883
-0.036358
0
0
0
0
Spherical-aberration-like terms
0.024071
0.025429
0.025068
0.024914
0
0.003675
0.003480
0.001006
0.048142
0.050568
0.048516
0.045002
0
0.024071
Grid size
0.083416
0.083296
0.083296
0.081375
All results are for a undistorted grid, with a 1-mm grid spacing, placed 30 mm from the anterior corneal surface of the eye. The subgrid values were the same as those for a whole grid with the corresponding weights set to zero.