2 CYCLICAL SHEARING INTERFEROMETER

Transcription

1 2 CYCLICAL SHEARING INTERFEROMETER Collimation Testing and Measurement of The Radius of Curvature of the Wavefront MODEL OEK-100 PROJECT #1

2 Introduction In many applications, it is desired to measure the aberration in a wavefront. By probing these aberrations the quality of the media through which a collimated light beam passed or has been reflected from may be measured. In the case of optical components, the testing of lenses and reflectors may easily be accomplished by measuring the quality of the wavefront. A method of measuring the wavefronts consists of taking the beams that have passed through or been reflected from the object under study, displacing the beam and interfering them in an appropriate interferometric configuration. Michelson, Mach-Zehnder, Sagnac interferometer configurations have all been used. Fringes are produced when the beams interfere. However since the two wavefronts are affected identically by the optical surface under test, some shear is required to produce a measurable mismatch between the beams so to show up aberrations in the wavefronts. In a common beam shearing interferometer which may be implemented in the Sagnac interferometer configuration used in this experiment (Figure 5), the same beam is divided, shifted and then recombined producing what is known as the auto correlation method i.e. for the one dimensional case. II is given by I E11 2. This may be rewritten as 1= 21 1 [1 + F(st) cos (q,-8( '))] where<\> is any arbitrary phase shift between the two beams, F(s') is the correlation functions modulus and 8 (s') is the phase shift due to the wavefront curvature and normalized shear s'. If <\> is varied, the second term in I varies sinusoidally with amplitude F and phase offset 8. By varying the shear S', the total intensity of the overlapping beams (see Figure 4) varies yielding the tenn F(s') and 8(s'). Examination of these fringes will provide detailed information as to the aberrations in the bean. For the Cyclical Shealing Interferometer studied in this experiment, the two dimensional derivation of the above equation with all the details for the wavefronts used is presented in reference [2.1].

3 19 Screen Figure 5 L BE M2 Figure 6

4 Equipment list Part Number Description QTY 1476S-01 Ball Driver Set 1 SK-OSA Screw Kit 1 SK-25A Screw Kit 1 RG 'x3' Breadboard 1 BE. Beam Expander Assembly B-2SA Base Plate 1 LC-V Collimator Module 1 M-40X Objective Lens 1 MH-2PM Objective Mount 1 SP-3 3" Post 1 SP-4 4" Post 1 VPH-3 3" Post Holder 1 VPH-4 4" Post Holder 1 BS. Beamsplitter Assembly 20B20BS.1 2" Beamsplitter 1 U200-A2K Mirror Mount 1 SP-3 VPH-3 CT. Collimation Tester Assembly 3" Post 1 3" Post Holder 1 20QS20 2" Collimation Tester 1 AC-2A Lens Mount 1 B-2SA Base Plate 1 SP-3 3" Post 1 VPH-3 3" Post Holder 1 I. Iris Assembly Iris 2 MCF Flat Carrier 2 MH-2P Iris Mount 2

5 21 MSP-3 3" Post 2 MPH-3 3" Post Holder 2 MRL-3 Micro Optical Rail 1 MRL-18M Micro Optical Rail 1 L. Laser Assembly 340-RC Clamp 1 40 Rod 1 ULM-TILT Laser Mount 1 R mw HeNe Laser 1 MS. Steering Mirror Assembly 10D20ER.1 1" Mirror 1 COR-1 Cntr Of Rotatn Adaptr 1 P100-P Mirror Mount 1 UPA1 1" Mirror Holder 1 SP-3 3" Post 1 VPH-3 3" Post Holder 1 M1 and M2. Mirror Assemblies 20D20ER.1 2" Mirror 2 U200-A2K Mirror Mount 2 SP-3 3" Post 2 VPH-3 3" Post Holder 2 Screen Assembly B-2SA Base Plate 1 BC-5 Base Clamp 1 FC-1 Filter Clamp 1 SP-2 VPH-2 2" Post 1 2" Post Holder Setup Placement of the Breadboard Place the RG-23-4 breadboard on a flat stable surface. Make sure that there is enough surface area near the breadboard to place the power supply units and other items that need not be mounted.

6 Laser Setup Mount a 40 Rod on the RG-23-4 breadboard in location L as in Figure 5 (Figure 6). Attach a ULM-TILT Laser Mount to a 340-RC lamp. Slide the 340-RC onto the 40 Rod. Mount the R laser head in the ULM-TIL T mount and align the laser tube so that the polarization plane is perpendicular to the table top ("S" polarization) Laser Beam Alignment Post mount the Iris Assembly I on the MRL-3 Rail. Tum on the laser, point the beam along the long side of the breadboard and adjust the laser height to 6 inches. Place the iris directly in front of the laser head (position II in Figure 7 with its aperture aligned with the laser beam. Move the iris to the other end of the breadboard (position lz in Figure 7) and adjust tilt and vertical position of the laser on the post to align the beam with the iris aperture. Move the Iris back and forth between positions II and h to ensure that the beam is parallel to the surface of the breadboard. The MRL-18M can also be used with both iris assemblies on it, and the laser beam can be easily aligned with the two iris apertures. Once the tilt of the laser is set the height can be varied by the 340-RC clamp and the beam will still be parallel to the surface of the breadboard Iris Placement Affix ID-0.5 iris I in front of the laser as shown in Figure 8 and adjust the aperture to just allow the laser beam through. The iris will now be used as a reference for retroreflected beams Interferometer Setup Choose one of the setup configurations, Figure 5 or Figure 6 (Figure 6 is an alternative for the setup of Figure 5 which increases the cross section of the optical windows). Place the 20D20ER.l 2" diameter mirrors and the 20B20BS.l beam splitter into the U200-A2K mounts and post mount each in place as shown in Figure 6 or Figure 8, to construct the Cyclical Shearing Interferometer. Use 1/4-20 set screws on the SP-3 posts to connect to U200 A2K mirror mounts. Post mount each interferometer mirror 10" from the beam splitter Interferometer Alignment Center the beam on BS optic and on MI by adjusting their post heights. Check the beam height in front of mirror MI. Ifbeam height is not the same before and after the beamsplitter, adjust the tilt of the beam splitter until the beam is horizontal. Place the iris assembly I in front ofmirror M2, match the height of the beam by adjusting the beamsplitter and MI respectively Beam Expander Positioning Assemble the beam expander assembly BE and mount in the path of the laser beam. Attach the SP-3 post to the B-2SA base and mount the LC-V collimating lens directly onto the B-2SA base. Place the VPH-3 post holder on the breadboard so that when the LC-V is put in place there will be some

7 room left to mount the M-40X objective lens (see Figure 9 for positioning of the Obj ctive lens). Mount the M-40X objective lens directly behind the LC V. Tum on the laser and adjust the height of the LC-V until the beam is centered 011 the I ns. Insert the M-40X objective lens in its place and align so that the expanding beam is centered on the collimating lens of the LC-V. Collimation Calibration Place the collimation tester (model No 20QS20) in an AC-2A optics mount (use proper support stud tips in the AC-2A). NOTE The collimation tester is a wedged plate with its thicker side marked on the edge. It is desirable to have the thick edge of the plate pointing to the top of the AC-2A Place the Collimation Tester Assembly CT at a 45 angle in the path of the expanded beam and look for fringes in the reflection. Adjust the position of the collimating lens in the beam expander until horizontal fringes are observed in the reflection. There should be three to five fringes visible in the reflection when fringes are horizontal. At this stage the expanded beam is well collimated. Adjustments Place a screen (i.e. a 3" X 5" card) into a FC-I filter clamp and Post mount on a SP-2 post, VPH-2 post holder, at the output of the interferometer and adjust the tilt of the mirrors and beam splitter while looking at the retroreflection on the iris. When the points of light are superimposed on the iris, fringes can be observed on the screen. Further adjustment should be made so that horizontal fringes are observed on the screen. (For more information see reference [2.1]) --Il --I2 " Figure 7

8 24 L I ". MS I II Figure 8 L I II] *Placement of 13 in this position is temporary (see instruc tion s)... MS Figure Procedure and results 1. The horizontal fringes obtained in the previous stage can be used as a reference for collimation of other laser beams and calculation of radius of divergence of the collimation. Once the Cyclical Shearing Interferometer is set as described, it is calibrated and should not be further adjusted. 2. Data acquisition Change the collimation of the beam by turning the collimating lens in increments of 114 tum (a small pencil mark on the collimating lens housing can be used for counting tum increments). Each 1/4 tum is equivalent to a linear displacement of mm which is calculated from the pitch of the collimator lens threads. Tum the lens 114 tum and trace out the resulting fringe pattern on a graph paper. The paper needs to be placed on the screen so that the grid lines run along the horizontal and vertical axes and will be used as a reference to measure the angle the fringes will make with the horizontal axis, ~. Note that if the fringes tum beyond 90 the angle ~ is still measured from the horizontal and the recorded angle will be larger than ~

9 25 3. With th graph paper still in position, plac the iris assembly in front of the collimating lens, position h and close the iris aperture to minimum diameter. Move the iris around until two illuminated points are visible on the paper. Thes points are due to the shear of the mirrors. Mark the relative position of these two points making sure that the vertical and horizontal refer nces are still aligned. The vertical and horizontal distance between the points are the vertical and horizontal shear of the interferometer respectively, which will be used in the formulas in the following section. 4. Recalibrate the beam expander using the collimation tester (part No 20QS20) and trace out a few more fringe patterns for multiple increments of 114 turn of the co llimating lens. 5. Change the shear of the interferometer by changing the 2"minors and beam splitter tilt adjustments. Place the Iris Assembly as in step 3 and try to increase the horizontal distance between the two points to more than 10.0 mm. This will yield three significant figures for the shear and the accuracy of the calculation is improved. 6. As indicated in the theory (and also in the reference) the radius of the divergence of the beam can be calculated. Other parameters can also be calculated as described below. 7. The fringe spacing, d, can be measured and used (see Figure 10) in the following formulas to find the tilt in beam splitter and the first minor. A d=- L vs (2.1) e (1 - R) + If where Ais the wavelength of light used, e is the vertical tilt angle between the two exiting beams, L is the path length for one arm of the interferometer, vs is the vertical shear measured on the screen, and R is the radius of divergence or convergence of the collimated beam. Figure 10 For calibrated horizontal fringes, R is infinite so that the folmula is reduced to A d=e

10 26 The second formula used is the relation between the angle 8 and \jf (2.2) where \jf is the tilt on the beam splitter. Combining the last two equations by eliminating 8 we get 2_ A 'V - 2~ d The path length difference, i'll, in the interferometer can be found from the following equation (derived numerically in reference [l.i]) LlL = L 'V 2 (2.3) where L is the distance between the beam splitter and the two mirrors. From these values the temporal difference Llt=LlL/c can be calculated which is the limiting value for the minimum coherence time that will produce fringes with good visibility in the interferometer. 8. The experimental radius ofcurvature of the collimated beam, where s is the horizontal shear measured on the screen, s d Rexp=--- (2.4) A tancp can be compared with the theoretical value calculated from the Guassian lens formula where =-+f do di do = f + 0 and where 8 is the small displacement of the collimating lens of the beam expander. The collimating lens on the beam expander has a focal length f, where do and d i are the object and image distance respectively. This small value of 8 can be accomplished by rotating the collimating lens by one or two whole turns which will change the radius of the beam. By comparing the relative magnitude of the variables in the above equations, we can approximate the theoretical radius by the equation f2 R theory =di ::; o 9. The CSI was used in this experiment to collimate a HeNe laser beam. This setup, once calibrated as mentioned in the setup and procedure section, can be used to collimate other types of lasers with much shorter coherence length. The CSl does not need to be further modified and only the laser needs to be aligned so that the fringes are observed. Note that the fringe spacing d is a function of the wavelength of the laser.

11 Defin itions of Terms c Spe d of light x 10 8 mls CSI Cycli aj Shearing Interferometer 8 Small linear displacement in the collimating lens d Ve11ical fringe spacing d i do f Image distance to the collimating lens Object distance to the collimating lens Focal length of the collimating lens <P The angle measured from the horizontal of the resulting fringes L Path length for one arm of the interferometer ~L Path length difference between the two arms of the interferometer Ie Wavelength of the laser light used 8 Vertical tilt angle between the two exiting beams from the beam splitter R s Radius of divergence or convergence of the collimated beam Horizontal shear measured on the screen ~t Temporal difference due to ~L vs \ji Vertical shear measured on the screen Horizontal tilt angle on the beam splitter 2.6 References [2.1] T. D. Henning and 1. L. Carlsten, "Cyclical shearing interferometer for collimating short coherence-length laser beams," Appl. Opt. 31, (1992). [2.2] P. Hariharan, Optical Intelierometry, Academic Press, Sydney (1985). [2.3] P. Hariharan, Basics ofinterferometry, Academic Press, San Diego ( 1992). [2.4] F. A. Jenkins and H. E. White, Fundamentals o/optics, McGraw Hill, New York (1976). [2.5] E. Hecht, Optics, Addison-Wesley, Reading MA (1987).