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Testing Absolute Absolute measurement of flats Absolute measurement of flats Absolute measurement of spheres Absolute measurement of spheres Absolute measurement of surface roughness Absolute measurement of surface roughness James C. Wyant Absolute Surface Shape Measurement Removing system aberrations & Removing system aberrations & reference surface effects reference surface effects Improves measurement accuracy Improves measurement accuracy Tests for Tests for Flats Flats Spheres Spheres Surface roughness Surface roughness James C. Wyant ThreeFlatTest.nb James C. Wyant (2003) 1 Three-Flat Test If we have only two flats and we get straight line fringes when we compare the two flats we do not know they are flat because one could be concave and the second could be convex so the two surfaces match. If we have three flats and we get straight line fringes when we compare flat A with flat B and when we compare flat A with flat C and again when we compare flat B with flat C then the surfaces must all be flat. The following are the four measurements required to find an absolute measurement of the x and y profiles of the three flats. x B Inverted A x x C Inverted A x x C Inverted B x x x C Inverted B Rotated From the 4 measurements we obtain GAC @x_, y_D := fA @x, yD + fC @-x, yD GBC @x_, y_D := fB @x, yD + fC @-x, yD GAB @x_, y_D := fA @x, yD + fB @-x, yD Using the first, second, and third measurements we can solve for the y profiles. GBC' @x_, y_D := fB @-x, -yD + fC @-x, yD AB B B B B A AC C C C C A BC C C C C B ThreeFlatTest.nb GAB @0, yD + GAC @0, yD - GBC @0, yD 2 2 James C. Wyant (2003) 2 -GAB @0, yD + GAC @0, yD + GBC @0, yD 2 GAB @0, yD - GAC @0, yD + GBC @0, yD = fA @0, yD = fB @0, yD Using the first, second, and fourth measurements we can solve for the x profiles. = fC @0, yD AB B B B A AC C C C = fA @x, 0D 2 = fB @-x, 0D BC' A C C C B GAB @x, 0D - GAC @x, 0D + GBC' @x, 0D 2 2 We have obtained the x and y profiles of the three flats. The process can be repeated to obtain other profiles. -GAB @x, 0D + GAC @x, 0D + GBC' @x, 0D GAB @x, 0D + GAC @x, 0D - GBC' @x, 0D = fC @-x, 0D Absolute Sphere Testing.nb James C. Wyant (2003) 1 Absolute Sphere Testing Using the following procedure it is possible to separate interferometer errors from errors in the spherical mirror being tested. The technique will work with both the Twyman-Green interferometer and the laser-based Fizeau interferometer. Three measurements are required. W 0 W 180 W The focus three measurements give W180 @x_, y_D := 2 Wsurf @-x, -yD + Wref @x, yD + 2 Wdiv @x, yD Wfocus @x_, y_D := Wref @x, yD + Wdiv @x, yD + Wdiv @-x, -yD 1 4 HW0 @x, yD + W180 @-x, -yD - Wfocus @x, yD - Wfocus @-x, -yDL = Wsurf @x, yD W0 @x_, y_D := 2 Wsurf @x, yD + Wref @x, yD + 2 Wdiv @x, yD The mirror surface error is given by @-x.- yD in the last equation means we are rotating the data 180 in the computer. Single Measurement of Sphere TILT, POWER REMOVED INTERVAL = 0.025 RMS = 0.014 WAVES P-V = 0.121 WAVES FIZEAU INTERFEROMETER, F/1.1 REF. SPHERE James C. Wyant Flat at Focus f/1.1 Diverger TILT, POWER, COMA REMOVED INTERVAL = 0.05 RMS = 0.027 WAVES P-V = 0.243 WAVES James C. Wyant Absolute Reference TILT, POWER REMOVED INTERVAL = 0.025 RMS = 0.010 WAVES P-V = 0.084 WAVES James C. Wyant Absolute Measurement of Sphere TILT,POWER REMOVED INTERVAL = 0.025 RMS = 0.011 WAVES P-V = 0.081 WAVES James C. Wyant Absolute Surface Roughness Measurement Assumptions Surface height is random Surface height is random Statistics do not vary over surface Statistics do not vary over surface Each measurement = Test + Reference Each measurement = Test + Reference Test and reference uncorrelated Test and reference uncorrelated RMSmeas= James C. Wyant 2 2 + RMStest RMSref Effect of Reference Surface on Measurement Error in measured rms for 5 A rms reference surface 6 4 2 0 0 5 10 15 20 25 30 Rms roughness of test surface (A) James C. Wyant Subtraction of Errors due to Reference Surface Perfect mirror Perfect mirror Generate reference Generate reference Absolute rms measurement Absolute rms measurement James C. Wyant Generate Reference Average many measurements Average many measurements Move random surface > correlation Move random surface > correlation length between measurements length between measurements Effects of random surface reduce as Effects of random surface reduce as square root of number of measurements square root of number of measurements James C. Wyant Generate Reference and Subtract Surface + Reference Reference Surface (0.071 nm) James C. Wyant Absolute RMS Measurement Make 2 measurements where surface moved > correlation length between measurements Subtract measurements and divide by square root of 2 Reference cancels and obtain RMS of test surface Diff = Test1+ (-Test2 ) 1 RMSTest = 2 RMSDiff James C. Wyant Generate Reference and Absolute RMS Comparison Generate Reference Absolute RMS RMS = 0.071 nm RMS = 0.070 nm James C. Wyant

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