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Polarization Errors Associated with Birefringent Waveplates

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Polarization Errors Associated with Birefringent Waveplates Polarization errors associated with birefringent waveplates Edward A. West Abstract. Although zero-order quartz waveplates are widely used in in- Matthew H. Smith strumentation that needs good temperature and field-of-view character- NASA/Marshall Space Flight Center istics, the residual errors associated with these devices can be very im- Space Sciences Laboratory portant in high-resolution polarimetry measurements. How the field-of- ES82 view characteristics are affected by retardation errors and the misalign- Marshall Space Flight Center, Alabama ment of optic axes in a double-crystal waveplate is discussed. The re- 35812 tardation measurements made on zero-order quartz and single-order E-mail: [email protected] "achromatic" waveplates and how the misalignment errors affect those measurements are discussed. Subject terms: polarization analysis and measurement; waveplates; retardation;' polarimetry. Optical Engineering 34(6), 1574-1580 (June 1995). (NASA-TM-111220) POLARIZATION N96-17862 ERRORS ASSOCIATED WITH BIREFRINGENT WAVEPLATES (NASA. Marshall Space Fl ight Center) 7 p Unclas G3/7A 0098274 1 Introduction solute retardance. Section 3 describes the errors associated In almost any device that measures polarization, waveplates with multiple plate retarders and Sec. 4 presents the data that seem to be a necessary evil. They may be used as one of the were obtained on the experimental vector magnetograph active elements in a polarization analyzer (for example, a (EXVM) waveplates. 1 2 rotating quarter-wave plate ' ) or in the calibration of the 2 Test Equipment polarization analyzer (for example, KD*P electro-optic crystal3). As the accuracy of polarization measurements is Figure 1 shows the optical components that were used in the pushed below 10 ~2, errors that might normally be neglected retardation measurements. One of the main problems in test- in waveplates become important, and determining the source ing any polarization element is obtaining a perfect input po- of those errors so that models can be developed to study and larizer and a perfect analyzer. In the visible spectrum, prism eliminate them becomes a complicated task. polarizers have the highest polarization resolution. To pro- In instruments that measure polarized light very accu- duce a "perfect" polarization source, two Glan-Thompson rately, "known" polarizations are used as the input source, polarizers were aligned in parallel and were placed in front measurements are made with the polarimeter, and the Mueller of the waveplate to be tested. The "perfect" analyzer was matrix relating the input to the output is determined. This the EXVM polarimeter which consists of a Glan-Thompson paper discusses the test equipment used and the data that polarizer and an HN32 Polaroid whose transmission axes 4 were obtained on quarter-wave plates, which will be used in were also aligned parallel. the development of a polarimeter for solar magnetic field A multiline HeNe laser was used as the light source and measurements. Section 2 describes the test equipment and a beam expander was added to the laser to produce a 13-mm some of the problems that occurred in determining the ab- collimated beam. A shutter and an achromatic waveplate were placed between the linearly polarized laser and the calibration polarizer. Paper PAM-07 received Oct. 31, 1994; revised manuscript received Jan. 9, 1995; accepted for publication Jan. 26, 1995. This paper is a revision of a paper presented A photomultiplier (PM) tube was used as the detector. The at the SPIE conference on Polarization Analysis and Measurement II, July 1994, PM tube was selected because of its sensitivity to low light San Diego, CA. The paper presented there appears (unrefereed) in SPIE Proceedings Vol. 2265. levels. Because PM tubes are not known for their linearity © 1995 Society of Photo-Optical Instrumentation Engineers. 0091-3286/95/$6.00. and the input source (the multiline HeNe laser) was not stable, 1574 /OPTICAL ENGINEERING / June 1995 /Vol. 34 No. 6 PRECEDING PAGE NOT. FILMED POLARIZATION ERRORS ASSOCIATED WITH BIREFRINGENT WAVEPLATES' '*"'"' multi-line calibration EXVM HeNe laser polarizer analyzer PM tube collimating shutter calibration EXVM Babinet blocking lens \i. X; Compensator filter M '4 /\/\/v Fig. 1 Optical equipment used to test the EXVM quarter-wave plates. OA, OA« OA« a Soleil-Babinet compensator was used to measure the re- Fixed Variable tardation of the EXVM waveplates. To minimize detector Retarder Retarder and source errors, all calibration points and retardation mea- Fig. 2 Optical elements that make up a Soleil-Babinet compensator. surements were made at minimum signal levels and as rapidly as possible. With the detector and source errors minimized, the Soleil-Babinet compensator became the next critical error fringence. Because these errors are dependent on the expe- source. rience of the company manufacturing the waveplates (and In the following discussion, "optical axis" refers to the the user to detect them), they are neglected and the following propagation direction of the light. "Optic axis" refers to the assumptions are made: (1) there is no variation in the optical direction in a birefringent crystal in which there is no phase properties in the birefringent crystals used to produce the retardance for light propagating along that axis. For biaxial waveplates, (2) the aperture size of the retarder is much larger crystals, there are two "optic axes." For uniaxial crystals, than the incident light so that edge effects can be neglected, which are used in the construction waveplates, there is one and (3) the waveplates forming the retarder have parallel optic axis direction and it is parallel to the extraordinary index surfaces. The remaining errors are thickness, field-of-view of refraction (ne). Therefore, to change polarized light, the errors, optic axis tilt errors, and fast axis misalignments. "optic axis" of a waveplate is perpendicular to the "optical These errors are shown in Fig. 3. Before describing these axis" of the lens system. errors, a short discussion on the two types of waveplates that The optical components of a Soleil-Babinet compensator were selected for use in the EXVM polarimeter is in order. are shown in Fig. 2. The compensator consists of three quartz plates, one plane parallel plate and two plates with a 2.5 deg 3.1 Description of the EXVM Waveplates wedge. The optic axis (OA) of the parallel plate is perpen- dicular to the optic axes of the two wedge plates, and one of Figure 4 shows the structure of the zero-order and achromatic the wedge plates is allowed to move. The parallel plate has waveplates used in the EXVM magnetograph. The zero-order a fixed retardance, whereas the two wedges form a variable waveplates are standard quartz waveplates in which the optic waveplate whose retardance is dependent on the total thick- axes (the extraordinary indices, ny and n'x, in Fig. 4) of the ness of the two wedges. The parallel plate retarder is com- two quartz crystals are perpendicular to the propagation of bined with the wedge retarder to minimize the variation of the light (optical axis) and are separated by 90 deg. This retardance over the field of view. As one would expect, the orientation minimizes field-of-view errors and the retardation main error in the Soleil-Babinet compensator is the posi- is simply related to the difference in the thickness of the two tioning of the moveable wedge. These include both rotational plates. Although the relationship of retardance to thickness misalignment errors of the optic axes of the two wedges and is normally written as translational errors (a thickness/optical path error, which translates into a retardation error). To minimize the trans- C (1) lation and rotational errors in the compensator, the moveable waveplate was only allowed to move in one direction to minimize mechanical backlash in its positioning. Finally, the we use a longer notation so that the errors to be discussed compensator was calibrated before and after every set of fast can be related to that equation. Therefore, the equation for a axis retardation measurements (at 45,135,225, and 315 deg) zero-order or achromatic retarder is written in the form made on the test waveplate. This was done to eliminate any systematic dc offsets in the retardation measurements. '- n'x)d2 o = 1 (2) 3 Modeling Retarder Errors There are some errors that depend on the quality control in or the construction phase of the retarder that are difficult to model and are neglected here. One error that is neglected is = S1-f-S2 (3) the crystalline structure of the birefringent material used to produce the waveplate. This error is dependent on the ex- where nx is the ordinary index of refraction, ny is the extra- perience of the optician and the availability of high-quality ordinary, and 8, is the total retardance of the first waveplate crystals. Other errors are related to the manufacturing process (WP1). Similarly, ny is the ordinary, n'xthe the extraordinary, such as roll-off effects at the edge and stress-induced bire- and 82 the total retardance of the second waveplate (WP2). OPTICAL ENGINEERING / June 1995 /Vol. 34 No. 6 / 1575 WEST and SMITH (c) Fig. 3 Schematic of the various errors considered: (a) thickness error, (b) field-of-view errors, (c) optic axis tilt errors, and (d) fast axis misalignment. , The achromatic waveplates have the same optic axis align- ment as the quartz waveplates, but one of the quartz plates is replaced with a magnesium fluoride (MgF2) plate. Both quartz and MgF2 are positive uniaxial crystals (ne>n0). Al- though termed an achromatic waveplate, the design goal was to achieve a quarter-wave retardance at 5250 and 6302 A. Therefore, the thicknesses for the MgF2 and quartz plates were adjusted to meet those design specifications. Table 1 shows the optical properties that would be required to obtain perfect zero-order and achromatic waveplates.
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