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Polarization Optics Test Plan Document PROC-0027 Revision B Polarization Optics Test Plan Stacey Sueoka, Dave Harrington, Andy Ferayorni PA&C Team 23 January 2019

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Page 1: PROC-0027 Polarization Optics Test Plan - DKIST...Polarization Optics Test Plan PROC-0027, Revision B Page 2 of 56 2. PRELIMINARY RETARDER TESTING 2.1 OVERVIEW Meadowlark Optics Inc

Polarization Optics Test Plan Document PROC-0027

Revision B

Polarization Optics Test Plan

Stacey Sueoka, Dave Harrington, Andy Ferayorni PA&C Team

23 January 2019

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REVISION SUMMARY: 1. Date: 19 March 2016

Revision: Draft A Changes: Initial release

2. Date: 2 February 2017 Revision: A Changes: Update to match latest requirements per CMX. Add additional level of detail to each procedure. Initial formal release.

3. Date: 18 December 2017

Revision: A

Changes: Updates for CDR on all acceptance tests

4. Date: 23 January 2019

Revision: B

Changes: Updated procedures for calibration optical elements prior to LAT

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Table of Contents

1.  INTRODUCTION ................................................................................................... 1 1.1  SCOPE ................................................................................................................... 1 1.2  REFERENCED DOCUMENTS ...................................................................................... 1 2.  PRELIMINARY RETARDER TESTING ................................................................ 2 2.1  OVERVIEW .............................................................................................................. 2 2.2  ENVIRONMENT ........................................................................................................ 2 2.3  TESTS .................................................................................................................... 2 2.3.1  Modulator: Wavelength Range – ViSP .......................................................................... 3 2.3.2  Modulator: Wavelength Range – DL-NIRSP.................................................................. 4 2.3.3  Modulator: Wavelength Range – Cryo-NIRSP .............................................................. 5 2.3.4  Calibration Retarders: Wavelength Range ................................................................... 6 2.3.5  Modulator: Reflectivity and Transmission – ViSP ........................................................ 7 2.3.6  Modulator: Reflectivity and Transmission – DL-NIRSP ............................................... 8 2.3.7  Modulator: Reflectivity and Transmission – Cryo-NIRSP ........................................... 9 2.3.8  Calibration Retarders: Reflectivity and Transmission ............................................... 10 2.3.9  Modulator: Aperture – ViSP ......................................................................................... 11 2.3.10  Modulator: Aperture – DL-NIRSP ................................................................................. 12 2.3.11  Modulator: Aperture – Cryo-NIRSP ............................................................................. 13 2.3.12  Calibration Retarders: Aperture .................................................................................. 14 2.3.13  Modulator: Optical Polish ............................................................................................. 15 2.3.14  Calibration Retarders: Optical Polish.......................................................................... 16 2.3.15  Modulator: Transmitted WFE – ViSP ........................................................................... 17 2.3.16  Modulator: Transmitted WFE – DL-NIRSP .................................................................. 18 2.3.17  Modulator: Transmitted WFE – Cryo-NIRSP ............................................................... 19 2.3.18  Calibration Retarders: Transmitted WFE .................................................................... 20 2.3.19  Modulator: Beam Deflection Angle – ViSP ................................................................. 21 2.3.20  Modulator: Beam Deflection Angle – DL-NIRSP ......................................................... 22 2.3.21  Modulator: Beam Deflection Angle – Cryo-NIRSP ..................................................... 23 2.3.22  Calibration Retarder: Beam Deflection Angle ............................................................ 24 2.3.23  Modulator: Retardance at Normal Incidence .............................................................. 25 2.3.24  Calibration Retarders: Retardance at Normal Incidence ........................................... 26 2.3.25  Modulator: Retardance Uniformity .............................................................................. 27 2.3.26  Calibration Retarders: Retardance Uniformity ........................................................... 28 2.3.27  Modulator: Retarder Bias Plate Thickness – ViSP ..................................................... 29 2.3.28  Modulator: Retarder Bias Plate Thickness – DL-NIRSP ............................................ 30 2.3.29  Modulator: Retarder Bias Plate Thickness – Cryo-NIRSP ......................................... 31 2.3.30  Calibration Retarders: Retarder Bias Plate Thickness – ViSP .................................. 32 2.3.31  Modulator: Clocking ..................................................................................................... 33 2.3.32  Calibration Retarders: Clocking .................................................................................. 34 2.3.33  Modulator: Optic Axis ................................................................................................... 35 2.3.34  Calibration Retarders: Optic Axis ................................................................................ 36 3.  FINAL RETARDER ACCEPTANCE TESTING ................................................... 37 3.1  OVERVIEW ............................................................................................................ 37 3.2  ENVIRONMENT ...................................................................................................... 37 3.3  TESTS .................................................................................................................. 37 3.3.1  Modulator: Wavelength Range – ViSP ........................................................................ 38 3.3.2  Modulator: Wavelength Range – DL-NIRSP................................................................ 39 

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3.3.3  Modulator: Wavelength Range – Cryo-NIRSP ............................................................ 40 3.3.4  Calibration Retarders: Wavelength Range ................................................................. 41 3.3.5  Modulator: Aperture – ViSP ......................................................................................... 42 3.3.6  Modulator: Aperture – DL-NIRSP ................................................................................. 43 3.3.7  Modulator: Aperture – Cryo-NIRSP ............................................................................. 44 3.3.8  Calibration Retarders: Aperture .................................................................................. 45 3.3.9  Modulator: Retardance at Normal Incidence .............................................................. 46 3.3.10  Calibration Retarders: Retardance at Normal Incidence ........................................... 47 3.3.11  Modulator: Retardance Uniformity .............................................................................. 48 3.3.12  Calibration Retarders: Retardance Uniformity ........................................................... 49 4.  CALIBRATION LINEAR POLARIZER ACCEPTANCE TESTING ..................... 50 4.1  OVERVIEW ............................................................................................................ 50 4.2  ENVIRONMENT ...................................................................................................... 50 4.3  TESTS .................................................................................................................. 50 4.3.1  Calibration Linear Polarizer: Wavelength Range ....................................................... 51 4.3.2  Calibration Linear Polarizer: Transmission ................................................................ 52 4.3.3  Calibration Linear Polarizer: Aperture ........................................................................ 53 4.3.4  Calibration Linear Polarizer: Optical Polish ............................................................... 54 4.3.5  Calibration Linear Polarizer: Transmitted WFE .......................................................... 55 4.3.6  Calibration Linear Polarizer: Beam Deflection Angle ................................................ 56 

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1. INTRODUCTION

1.1 SCOPE

This document describes the acceptance test plans for the PA&C polarization optics. These optics include the super achromatic retarders (SAR), poly chromatic modulators (PCM), and wire grid polarizers (WGP). SAR and PCM optics were made at Meadowlark Optics. Due to the complexity of these optical elements several steps in the acceptance and characterization were split into different documents. Section 2, preliminary tests describe the tests performed by the vendor and at NSO. These tests consist of individual plates in the retarder stack, and analysis of the assembled retarders in a prototype mount. This 3D printed mount allowed NSO to perform preliminary measurements of the polarization properties of the retarders. Any errors in the clocking of the crystal plates could be caught here and fixed with much less risk before finally gluing it into the metal cell. Section 3, acceptance testing describe the tests performed by the vendor and at NSO once the optic is mounted in its permanent metal cell. Section 4, acceptance testing describes the testing of the calibration linear polarizer. A new tech note, TN-XXX Characterization of PA&C Optics describes further characterization of the retarders and linear polarizer. In order to perform polarization systems engineering for DKIST, a thorough characterization of the retarders and linear polarizer Mueller matrices will be performed. Determine angle of incidence dependence, thermal stability, uniformity across the clear aperture, and durability/survivability of the assembly.

1.2 REFERENCED DOCUMENTS

PMCS-0024 ATST Acceptance Test Standards SPEC-0009 DKIST System Error Budgets (SEB) SPEC-0080 Gregorian Optical System Design Requirements Document (GOS DRD) SPEC-0116 Polarization Modulator Design Requirements Document (PMC DRD) SPEC-0134 Polarization Analysis and Calibration Specification (PA&C SPEC) TN-0180 Cryo-NIRSP Modulator TN-0181 Cryo-NIRSP Calibration Retarder TN-0182 ViSP Modulator TN-0183 ViSP Calibration Retarder TN-0191 DL-NIRSP Modulator TN-0192 DL-NIRSP Calibration Retarder TN-0231 Evaluating Laboratory Spectropolarimeter Performance TN-0286 IfA Maui Lab Spectropolarimeter Wire Grid Polarizer

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2. PRELIMINARY RETARDER TESTING

2.1 OVERVIEW

Meadowlark Optics Inc. is manufacturing the modulators for DKIST. For tests performed by NSO, Meadowlark delivers the optic in a 3D printed prototype mount. This is because mounting of a PCM optic into the final cell involves applying RTV and potting it into a metal cell. Once an optic is installed in the cells any issues with performance can only be corrected by removing the optic from the cell. The process of removing the optic from its cell is high risk, and likely will result in damage to the optic. Thus, prior to mounting the optic in the final cell the vendor will mount the optic in a temporary 3D printed cell, and deliver to the PA&C team for preliminary testing. The following is an outline of the preliminary tests that will be performed by the PA&C team in the lab at NSO, Boulder. The requirements covered by these tests are also indicated. These tests will be performed using the NSO Lab SpectroPolarimeter (NLSP) equipment described in TN-0231.

2.2 ENVIRONMENT

NSO measurements are performed in the NSO Boulder Lab, N130. Modular clean room, class 100,000. Measurements made with the NLSP visible spectrograph are binned to 75 wavelengths from 400 nm to 1100 nm.

Meadowlark measurements are performed at their facility, environment details in their reports.

2.3 TESTS

Tests described below are performed by NSO, Meadowlark Optics, and Stanford Photo-Thermal Solutions. Unless explicitly stated the measurements are performed by NSO.

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2.3.1 Modulator: Wavelength Range – ViSP

Type Test Requirement 3.1.1.6-0105-01, 3.1.1-0270, 3.1.1-0260 Preconditions PCM optic assembled  

PCM optic in prototype mount 

Test Steps Measure the Mueller matrix of the PCM with the NLSP 

Calculate the modulation efficiency over the measured wavelength range  

Using birefringence functions and measured data to extrapolate the modulation efficiency over the full ViSP wavelength range 

Plot the modulation efficiency as a function of wavelength to verify if the modulation efficiency meets requirement over the measured wavelength range 

Pass Criteria Modulator shall operate from 380 nm to 900 nm 

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes Goal modulator operation wavelength range is 380 nm to 1600 nm. If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm.

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2.3.2 Modulator: Wavelength Range – DL-NIRSP

Type Test Requirement 3.1.1.6-0105-02, 3.1.1-0270, 3.1.1-0260 Preconditions PCM optic assembled  

PCM optic in prototype mount 

Test Steps Measure the Mueller matrix of the PCM with the NLSP 

Calculate the modulation efficiency over the measured wavelength range  

Using birefringence functions and measured data to extrapolate the modulation efficiency over the full DL‐NIRSP wavelength range 

Plot the modulation efficiency as a function of wavelength to verify if the modulation efficiency meets requirement over the required wavelength range 

Pass Criteria Modulator shall operate from 900 nm to 2500 nm 

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes Goal modulator operation wavelength range is 500 nm to 2500 nm. If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm.

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2.3.3 Modulator: Wavelength Range – Cryo-NIRSP

Type Test Requirement 3.1.1.6-0105-03, 3.1.1-0270, 3.1.1-0260 Preconditions PCM optic assembled  

PCM optic in prototype mount 

Test Steps Measure the Mueller matrix of the PCM with the NLSP 

Calculate the modulation efficiency over the measured wavelength range  

Using birefringence functions and measured data to extrapolate the modulation efficiency over the full Cryo‐NIRSP wavelength range 

Plot the modulation efficiency as a function of wavelength to verify if the modulation efficiency meets requirement over the required wavelength range 

Pass Criteria Modulator shall operate from 1000 nm to 5000 nm 

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes Goal modulator operation wavelength range is 500 nm to 5000 nm. If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm. 

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2.3.4 Calibration Retarders: Wavelength Range

Type Test Requirement 3.1.1.3‐0041, 3.1.1‐0220, 3.1.1.3‐0135‐01, 3.1.1.3‐0135‐02, 3.1.1.3‐0135‐03, 3.1.1.3‐

0135‐04 Preconditions SAR optic assembled  

SAR optic in prototype mount 

Test Steps Measure the Mueller matrix of the SAR with the NLSP 

Calculate the linear retardance, circular retardance and fast axis orientation over the measured wavelength range  

Using birefringence functions and measured data to extrapolate the retardance over the full SAR wavelength range 

Plot the retarder parameters as a function of wavelength to verify if the linear retardance meets requirement over the measured wavelength range 

Pass Criteria ViSP(VTF) SAR shall operate from 380 nm to 900 nm 

DL‐NIRSP SAR shall operate from 900 to 2500 nm 

Cryo‐NIRSP SAR shall operate from 500 nm to 5000 nm 

NSO analysis of the data will verify if the retardance of the SAR assembly matches the design to within the tolerance of  0.01 waves thickness error in each of the pairs of crystal plates. 

Notes VTF operation wavelength range is 520nm to 870nm (Goal 500nm to 900nm). 

ViSP operation wavelength range is 380nm to 900nm (Goal 380nm to 1600nm).

DL‐NIRSP operation wavelength range is 900nm to 2500nm (Goal 500nm to 

2500nm). 

Cryo‐NIRSP operation wavelength range is 1000nm to 5000nm (Goal 500nm to 

5000nm). 

If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow 

us to perform measurements out to 1600 nm. 

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2.3.5 Modulator: Reflectivity and Transmission – ViSP

Type Test Requirement 3.1.1.6-0110-01 Preconditions PCM quartz plates are AR coated 

Test Steps Meadowlark will provide AR coating data 

Stanford PTS measures absorption at ppm level 

NSO will measure the transmission with NLSP from 400nm to 1100nm 

Pass Criteria Transmission shall be an average of 85% or better over the wavelength range 380 nm to 1800 nm.  

Notes If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm.

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2.3.6 Modulator: Reflectivity and Transmission – DL-NIRSP

Type Test Requirement 3.1.1.6-0110-02 Preconditions PCM quartz plates are AR coated 

Test Steps Meadowlark will provide AR coating data 

Stanford PTS measures absorption at ppm level 

NSO will measure the transmission with NLSP from 400nm to 1100nm 

Pass Criteria Transmission shall be an average of 85% or better over the wavelength range 380 nm to 1800 nm. 

Notes If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm.

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2.3.7 Modulator: Reflectivity and Transmission – Cryo-NIRSP

Type Test Requirement 3.1.1.6-0110-03 Preconditions PCM are AR coated 

Test Steps Meadowlark will provide AR coating data 

Stanford PTS measures absorption at ppm level 

NSO will measure the transmission with NLSP from 400nm to 1100nm 

Pass Criteria Transmission shall be an average of 85% or better over the wavelength range 1000 nm to 5000 nm. 

Notes If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm.

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2.3.8 Calibration Retarders: Reflectivity and Transmission

Type Test Requirement 3.1.1.3-0142 Preconditions SAR are AR coated 

Test Steps Meadowlark will provide AR coating data 

Stanford PTS measures absorption at ppm level 

NSO will measure the transmission with NLSP from 400nm to 1100nm 

Pass Criteria Over the broadband wavelength ranges required by polarization optics, surface reflection shall be reduced with anti‐reflection coatings. Individual optical interfaces shall be oiled with an index matching fluid and shall meet the following requirements: 

ViSP/DL‐NIRSP SAR: Surface reflection shall be less than an uncoated quartz surface for all wavelengths within its bass band and average <3% for all wavelengths. Transmission shall be an average of 85% or better over the wavelength range of 380nm to 2500nm. 

Cryo‐NIRS SAR: Surface reflection shall be less than or equal to that of an uncoated MgF2 surface for all wavelengths within its pass band and average <3% for all wavelengths. Transmission shall be an average of 85% or better over the wavelength range of 1000nm to 5000nm. 

Notes If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm.

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2.3.9 Modulator: Aperture – ViSP

Type Inspection Requirement 3.1.1.6-0115-01, 3.1.1-0270 Preconditions PCM optic assembled  

PCM optic in prototype mount 

Test Steps Inspected by Meadowlark 

Pass Criteria Clear aperture greater or equal to 90mm 

No significant cosmetic damage within the clear aperture  

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes NSO will measure modulation efficiency with the NLSP at the center of the clear aperture only during preliminary testing. Section 2.3 describes the test to verify if the modulation efficiency meets requirement over the measured wavelength range. Testing of modulation efficiency over the full clear aperture occurs during acceptance testing and is described in Section 0. 

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2.3.10 Modulator: Aperture – DL-NIRSP

Type Inspection Requirement 3.1.1.6-0115-02, 3.1.1-0270 Preconditions PCM optic assembled  

PCM optic in prototype mount 

Test Steps Inspected by Meadowlark 

Pass Criteria Clear aperture greater or equal to 81mm 

No significant cosmetic damage within the clear aperture 

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes NSO will measure modulation efficiency with the NLSP at the center of the clear aperture only during preliminary testing. Section 0 describes the test to verify if the modulation efficiency meets requirement over the measured wavelength range. Testing of modulation efficiency over the full clear aperture occurs during acceptance testing and is described in Section 0. 

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2.3.11 Modulator: Aperture – Cryo-NIRSP

Type Inspection Requirement 3.1.1.6-0115-03, 3.1.1-0270 Preconditions PCM optic assembled  

PCM optic in prototype mount 

Test Steps Inspected by Meadowlark  

Pass Criteria Clear aperture greater or equal to 105mm 

No significant cosmetic damage within the clear aperture 

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes NSO will measure modulation efficiency with the NLSP at the center of the clear aperture only during preliminary testing. Section 0 describes the test to verify if the modulation efficiency meets requirement over the measured wavelength range. Testing of modulation efficiency over the full clear aperture occurs during acceptance testing and is described in Section 0.

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2.3.12 Calibration Retarders: Aperture

Type Inspection Requirement 3.1.1.3-0140 Preconditions SAR optic assembled  

SAR optic in prototype mount 

Test Steps Inspected by Meadowlark 

Visual inspection by NSO, and Mueller matrix measurement  

Pass Criteria Clear aperture greater or equal to 105mm 

No significant cosmetic damage within the clear aperture  

NSO analysis of the data will verify if the retardance of the SAR assembly matches the design to within the tolerance of  0.01 waves thickness error in each of the pairs of crystal plates. 

Notes NSO will measure retarder properties with the NLSP at the center of the clear aperture only during preliminary testing. 

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2.3.13 Modulator: Optical Polish

Type Test Requirement 3.1.1.6-0120 Preconditions PCM plates are polished to design thickness 

Test Steps  Meadowlark inspects surface, provides photos and information about any defects on the surface 

Pass Criteria The optical quality of modulator optic exterior surfaces shall be 20/10 per MIL‐C‐48497A 

Notes

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2.3.14 Calibration Retarders: Optical Polish

Type Test Requirement 3.1.1.3-0052 Preconditions SAR plates are polished to design thickness 

Test Steps  Meadowlark inspects surface, provides photos and information about any defects on the surface 

Pass Criteria The optical quality of modulator optic exterior surfaces shall be 20/10 per MIL‐C‐48497A 

Notes

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2.3.15 Modulator: Transmitted WFE – ViSP

Type Test Requirement 3.1.1.6-0125-01 Preconditions PCM optic assembled 

Test Steps Test performed by Meadowlark 

Pass Criteria TWFE for ViSP shall be less than 3 waves P‐V at 633 nm power removed 

Notes

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2.3.16 Modulator: Transmitted WFE – DL-NIRSP

Type Test Requirement 3.1.1.6-0125-02 Preconditions PCM optic assembled 

Test Steps Test performed by Meadowlark 

Pass Criteria TWFE for DL‐NIRSP shall be less than 3 waves P‐V at 633 nm power removed 

Notes

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2.3.17 Modulator: Transmitted WFE – Cryo-NIRSP

Type Test Requirement 3.1.1.6-0125-03 Preconditions PCM optic assembled 

Test Steps Test performed by Meadowlark 

Pass Criteria TWFE for Cryo‐NIRSP shall be less than 2 waves P‐V at 633 nm power removed 

Notes

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2.3.18 Calibration Retarders: Transmitted WFE

Type Test Requirement 3.1.1.3-0080 Preconditions SAR optic assembled 

Test Steps Test performed by Meadowlark 

Pass Criteria TWFE  shall be less than 3 waves P‐V at 633 nm tip/tilt removed 

Notes

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2.3.19 Modulator: Beam Deflection Angle – ViSP

Type Test Requirement 3.1.1.6-0130-01 Preconditions PCM optic assembled 

Test Steps Test performed by Meadowlark 

Pass Criteria ViSP beam deflection shall be less than 90 arc seconds 

Notes

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2.3.20 Modulator: Beam Deflection Angle – DL-NIRSP

Type Test Requirement 3.1.1.6-0130-02 Preconditions PCM optic assembled 

Test Steps Test performed by Meadowlark 

Pass Criteria DL‐NIRSP beam deflection shall be less than 84 arc seconds 

Notes

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2.3.21 Modulator: Beam Deflection Angle – Cryo-NIRSP

Type Test Requirement 3.1.1.6-0130-03 Preconditions PCM optic assembled 

Test Steps Test performed by Meadowlark  

Pass Criteria Cryo‐NIRSP beam deflection shall be less than 10 arc seconds 

Notes

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2.3.22 Calibration Retarder: Beam Deflection Angle

Type Test Requirement 3.1.1.3-0050 Preconditions SAR optic assembled 

Test Steps Test performed by Meadowlark 

Pass Criteria Beam deflection shall be <96 arc seconds 

Notes

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2.3.23 Modulator: Retardance at Normal Incidence

Type Test Requirement 3.1.1.6‐0135, 3.1.1.6‐0100‐01, 3.1.1.6‐0100‐02, 3.1.1.6‐0100‐03 Preconditions PCM plates polished to design thicknesses 

PCM assembled (for NSO test) 

Test Steps Test performed by Meadowlark, retardance of each pair of crystal plates in the PCM is measured at normal incidence at 633.443 nm and 22 degree Celsius. 

NSO measures the Mueller matrix of the assembled PCM from 400nm to 1100nm at a single point on the clear aperture. Measurements are made at several AOI to determine the Mueller matrix of the PCM assembly in the NLSP at normal incidence to within ±0.5° 

NSO analysis of the data will verify if the retardance of the PCM assembly matches the design to within the tolerance of  0.01 waves thickness error in each of the pairs of crystal plates. 

Pass Criteria Retardance of each pair of crystal plates shall be 0.01 waves of the design retardance measured at 633.443 nm and 22° Celsius  

Notes

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2.3.24 Calibration Retarders: Retardance at Normal Incidence

Type Test Requirement 3.1.1.3‐0143, 3.1.1.3‐0135‐01, 3.1.1.3‐0135‐02, 3.1.1.3‐0135‐03, 3.1.1.3‐0135‐04  

Preconditions SAR plates polished to design thicknesses 

SAR assembled (for NSO test) 

Test Steps Test performed by Meadowlark, retardance of each pair of crystal plates in the SAR is measured at normal incidence at 633.443 nm and 22 degree Celsius. 

NSO measures the Mueller matrix of the assembled SAR from 400nm to 1100nm at a single point on the clear aperture. Measurements are made at several AOI to determine the Mueller matrix of the SAR assembly in the NLSP at normal incidence to within ±0.5° 

NSO analysis of the data will verify if the retardance of the SAR assembly matches the design to within the tolerance of  0.01 waves thickness error in each of the pairs of crystal plates. 

Pass Criteria Retardance of each pair of crystal plates shall be 0.01 waves of the design retardance measured at 633.443 nm and 22° Celsius  

Notes

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2.3.25 Modulator: Retardance Uniformity

Type Test Requirement 3.1.1.6-0140, 3.1.1.6-0100-01, 3.1.1.6-0100-02, 3.1.1.6-0100-03, 3.1.1-0270 Preconditions PCM plates polished to design thicknesses  

Test Steps Test performed by Meadowlark 

Pass Criteria For the Meadowlark test, the retardance uniformity of the pairs of plates shall be ±0.01 waves across the clear aperture 

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes Meadowlark will measure retardance at 5 positions on the clear aperture for each pair of plates. One in the center and four near the edges.  If retardance uniformity and clocking specifications are met by Meadowlark, then the modulation efficiency of the PCM will meet the requirement. Full aperture measurements with the NLSP in Section 0 will be performed during acceptance testing by NSO.  

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2.3.26 Calibration Retarders: Retardance Uniformity

Type Test Requirement 3.1.1.3‐0144, 3.1.1.3‐0135‐01, 3.1.1.3‐0135‐02, 3.1.1.3‐0135‐03, 3.1.1.3‐0135‐04

Preconditions SAR plates polished to design thicknesses  

Test Steps Test performed by Meadowlark 

NSO tests only a single aperture position 

Pass Criteria For the Meadowlark test, the retardance uniformity of the pairs of plates shall be ±0.01 waves across the clear aperture 

NSO analysis of the data will verify if the retardance of the SAR assembly matches the design to within the tolerance of  0.01 waves thickness error in each of the pairs of crystal plates. 

Notes Meadowlark will measure retardance at 5 positions on the clear aperture for each pair of plates. One in the center and four near the edges.  If retardance uniformity and clocking specifications are met by Meadowlark, then the retardance will meet the requirement. Full aperture measurements with the NLSP in Section 0 will be performed during acceptance testing by NSO.  

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2.3.27 Modulator: Retarder Bias Plate Thickness – ViSP

Type Test Requirement 3.1.1.6-0145-01 Preconditions PCM plates polished to design thicknesses  

Test Steps Test performed by Meadowlark. 

Pass Criteria The bias plate retardance shall be 30   1 waves 

Notes

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2.3.28 Modulator: Retarder Bias Plate Thickness – DL-NIRSP

Type Test Requirement 3.1.1.6-0145-02 Preconditions PCM plates polished to design thicknesses  

Test Steps Test performed by Meadowlark. 

Pass Criteria The bias plate retardance shall be 30   1 waves 

Notes

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2.3.29 Modulator: Retarder Bias Plate Thickness – Cryo-NIRSP

Type Test Requirement 3.1.1.6-0145-03 Preconditions PCM plates polished to design thicknesses  

Test Steps Test performed by Meadowlark. 

Pass Criteria The bias plate retardance shall be 40   1 waves 

Notes

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2.3.30 Calibration Retarders: Retarder Bias Plate Thickness – ViSP

Type Test Requirement 3.1.1.3‐0145‐01, 3.1.1.3‐0145‐02, 3.1.1.3‐0145‐03

Preconditions PCM plates polished to design thicknesses  

Test Steps Test performed by Meadowlark. 

Pass Criteria The bias plate retardance shall be 30   1 waves for ViSP and DL‐NIRSP 

The bias plate retardance shall be 40   1 waves for Cryo‐NIRSP 

Notes

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2.3.31 Modulator: Clocking

Type Test Requirement 3.1.1.6-0150, 3.1.1.6-0100-01, 3.1.1.6-0100-02, 3.1.1.6-0100-03, 3.1.1-0270 Preconditions PCM is assembled 

PCM in prototype mount 

Test Steps NSO measures the Mueller matrix of the assembled PCM from 400nm to 1100nm at a single point on the clear aperture. Measurements are made at several AOI to determine the Mueller matrix of the PCM assembly in the NLSP at normal incidence to within ±0.5° 

NSO analysis of the data will verify if the clocking of the PCM assembly matches the design to within the tolerance of  0. 3° clocking error between the crystal plates. 

Pass Criteria The fast axis of each crystal plate shall be aligned to  0.3° of the design clocking angle. 

Notes

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2.3.32 Calibration Retarders: Clocking

Type Test Requirement 3.1.1.3‐0146, 3.1.1.3‐0135‐01, 3.1.1.3‐0135‐02, 3.1.1.3‐0135‐03, 3.1.1.3‐0135‐04 

Preconditions SAR is assembled 

SAR in prototype mount 

Test Steps NSO measures the Mueller matrix of the assembled SAR from 400nm to 1100nm at a single point on the clear aperture. Measurements are made at several AOI to determine the Mueller matrix of the SAR assembly in the NLSP at normal incidence to within ±0.5° 

NSO analysis of the data will verify if the clocking of the SAR assembly matches the design to within the tolerance of  0. 3° clocking error between the crystal plates. 

Pass Criteria The fast axis of each crystal plate shall be aligned to  0.3° of the design clocking angle. 

Notes

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2.3.33 Modulator: Optic Axis

Type Test Requirement 3.1.1.6-0155 Preconditions PCM plates are polished to design thicknesses 

Test Steps Test performed by Meadowlark 

NSO Mueller matrix measurement and data reduction 

Pass Criteria The optic axis of each crystal plate shall be in the plane of the element  1.0°, single crystal, no twinning 

Measured Mueller matrix difference from the design is less than the estimated errors from a  1.0° optic axis tolerance 

Notes

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2.3.34 Calibration Retarders: Optic Axis

Type Test Requirement 3.1.1.3-0147 Preconditions SAR plates are polished to design thicknesses 

Test Steps Test performed by Meadowlark 

NSO Mueller matrix measurement and data reduction 

Pass Criteria The optic axis of each crystal plate shall be in the plane of the element  1.0°, single crystal, no twinning 

Measured Mueller matrix difference from the design is less than the estimated errors from a  1.0° optic axis tolerance 

Notes

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3. FINAL RETARDER ACCEPTANCE TESTING

3.1 OVERVIEW

Upon delivery of the optics from Meadowlark mounted in the final cell, a complete set of acceptance tests will be performed using the NLSP (see TN-0231) in the lab at NSO, Boulder. The following is a list of tests that will be performed and the requirements they cover.

3.2 ENVIRONMENT

NSO measurements are performed in the NSO Boulder Lab, N130. Modular clean room, class 100,000. Measurements made with the NLSP visible spectrograph are binned to 660 wavelengths from 380 nm to 1100 nm, and the NLSP IR spectrograph are binned to 255 wavelengths from 900 nm to 1650 nm.

Meadowlark measurements are performed at their facility, environment details in their reports.

3.3 TESTS

Tests described below are performed by NSO and Meadowlark Optics. Unless explicitly stated the measurements are performed by NSO.

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3.3.1 Modulator: Wavelength Range – ViSP

Type Test Requirement 3.1.1.6-0105-01, 3.1.1-0270, 3.1.1-0260 Preconditions PCM optic assembled  

PCM optic in final cell 

Test Steps Measure the Mueller matrix of the PCM with the NLSP 

Calculate the modulation efficiency over the measured wavelength range  

Using birefringence functions and measured data to extrapolate the modulation efficiency over the full ViSP wavelength range 

Plot the modulation efficiency as a function of wavelength to verify if the modulation efficiency meets requirement over the measured wavelength range 

Pass Criteria Modulator shall operate from 380 nm to 900 nm 

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes Goal modulator operation wavelength range is 380 nm to 1600 nm. If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm.

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3.3.2 Modulator: Wavelength Range – DL-NIRSP

Type Test Requirement 3.1.1.6-0105-02, 3.1.1-0270, 3.1.1-0260 Preconditions PCM optic assembled  

PCM optic in final cell 

Test Steps Measure the Mueller matrix of the PCM with the NLSP 

Calculate the modulation efficiency over the measured wavelength range  

Using birefringence functions and measured data to extrapolate the modulation efficiency over the full DL‐NIRSP wavelength range 

Plot the modulation efficiency as a function of wavelength to verify if the modulation efficiency meets requirement over the required wavelength rangeUsing birefringence functions and measured data to determine the modulation efficiency over the full DL‐NIRSP wavelength range 

Pass Criteria Modulator shall operate from 900 nm to 2500 nm 

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes Goal modulator operation wavelength range is 500 nm to 2500 nm. If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm.

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3.3.3 Modulator: Wavelength Range – Cryo-NIRSP

Type Test Requirement 3.1.1.6-0105-03, 3.1.1-0270, 3.1.1-0260 Preconditions PCM optic assembled  

PCM optic in final cell 

Test Steps Measure the Mueller matrix of the PCM with the NLSP 

Calculate the modulation efficiency over the measured wavelength range  

Using birefringence functions and measured data to extrapolate the modulation efficiency over the full Cryo‐NIRSP wavelength range 

Plot the modulation efficiency as a function of wavelength to verify if the modulation efficiency meets requirement over the required wavelength range 

Pass Criteria Modulator shall operate from 1000 nm to 5000 nm 

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes Goal modulator operation wavelength range is 500 nm to 5000 nm. If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm.

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3.3.4 Calibration Retarders: Wavelength Range

Type Test Requirement 3.1.1.3‐0041, 3.1.1‐0220, 3.1.1.3‐0135‐01, 3.1.1.3‐0135‐02, 3.1.1.3‐0135‐03, 3.1.1.3‐

0135‐04 Preconditions SAR optic assembled  

SAR optic in final cell  

Test Steps Measure the Mueller matrix of the SAR with the NLSP 

Calculate the linear retardance, circular retardance and fast axis orientation over the measured wavelength range  

Using birefringence functions and measured data to extrapolate the retardance over the full SAR wavelength range 

Plot the retarder parameters as a function of wavelength to verify if the linear retardance meets requirement over the measured wavelength range 

Pass Criteria ViSP(VTF) SAR shall operate from 380 nm to 900 nm 

DL‐NIRSP SAR shall operate from 900 to 2500 nm 

Cryo‐NIRSP SAR shall operate from 500 nm to 5000 nm 

NSO analysis of the data will verify if the retardance of the SAR assembly matches the design to within the tolerance of  0.01 waves thickness error in each of the pairs of crystal plates. 

Notes VTF operation wavelength range is 520nm to 870nm (Goal 500nm to 900nm). 

ViSP operation wavelength range is 380nm to 900nm (Goal 380nm to 1600nm).

DL‐NIRSP operation wavelength range is 900nm to 2500nm (Goal 500nm to 

2500nm). 

Cryo‐NIRSP operation wavelength range is 1000nm to 5000nm (Goal 500nm to 

5000nm). 

If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow 

us to perform measurements out to 1600 nm. 

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3.3.5 Modulator: Aperture – ViSP

Type Inspection Requirement 3.1.1.6-0115-01, 3.1.1-0270 Preconditions PCM optic assembled  

PCM optic in final cell 

Test Steps Inspected by Meadowlark  

Pass Criteria Clear aperture greater or equal to 90mm 

No significant cosmetic damage within the clear aperture  

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes NSO will measure modulation efficiency with the NLSP across the clear aperture. Mapping over the clear aperture is described in Section 0.

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3.3.6 Modulator: Aperture – DL-NIRSP

Type Inspection Requirement 3.1.1.6-0115-02, 3.1.1-0270 Preconditions PCM optic assembled  

PCM optic in final cell 

Test Steps Inspected by Meadowlark  

Pass Criteria Clear aperture greater or equal to 81mm 

No significant cosmetic damage within the clear aperture 

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes NSO will measure modulation efficiency with the NLSP across the clear aperture. Mapping over the clear aperture is described in Section 0.

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3.3.7 Modulator: Aperture – Cryo-NIRSP

Type Inspection Requirement 3.1.1.6-0115-03, 3.1.1-0270 Preconditions PCM optic assembled  

PCM optic in final cell 

Test Steps Inspected by Meadowlark  

Pass Criteria Clear aperture greater or equal to 105mm 

No significant cosmetic damage within the clear aperture 

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes NSO will measure modulation efficiency with the NLSP across the clear aperture. Mapping over the clear aperture is described in Section 0.

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3.3.8 Calibration Retarders: Aperture

Type Inspection Requirement 3.1.1.3-0140 Preconditions SAR optic assembled  

SAR optic in final cell 

Test Steps Inspected by Meadowlark 

Visual inspection by NSO, and Mueller matrix measurement  

Pass Criteria Clear aperture greater or equal to 105mm 

No significant cosmetic damage within the clear aperture  

NSO analysis of the data will verify if the retardance of the SAR assembly matches the design to within the tolerance of  0.01 waves thickness error in each of the pairs of crystal plates. 

Notes NSO will measure retarder properties with the NLSP across the clear aperture. Mapping over the clear aperture is described in Section 0.

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3.3.9 Modulator: Retardance at Normal Incidence

Type Test Requirement 3.1.1.6-0135, 3.1.1.6-0100-01, 3.1.1.6-0100-02, 3.1.1.6-0100-03 Preconditions PCM optic assembled  

PCM optic in final cell 

Test Steps NSO measures the Mueller matrix of the assembled PCM from 400nm to 1100nm at a single point on the clear aperture. Measurements are made at several AOI to determine the Mueller matrix of the PCM assembly in the NLSP at normal incidence to within ±0.5° 

NSO analysis of the data will verify if the retardance of the PCM assembly matches the design to within the tolerance of  0.01 waves thickness error in each of the pairs of crystal plates. 

Pass Criteria Retardance of each pair of crystal plates shall be 0.01 waves of the design retardance measured at 633.443 nm and 22° Celsius 

Notes

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3.3.10 Calibration Retarders: Retardance at Normal Incidence

Type Test Requirement 3.1.1.3‐0143, 3.1.1.3‐0135‐01, 3.1.1.3‐0135‐02, 3.1.1.3‐0135‐03, 3.1.1.3‐0135‐04  

Preconditions SAR optic assembled 

SAR optic in final cell 

Test Steps NSO measures the Mueller matrix of the assembled SAR from 400nm to 1600nm at a single point on the clear aperture. Measurements are made at several AOI to determine the Mueller matrix of the SAR assembly in the NLSP at normal incidence to within ±0.5° 

NSO analysis of the data will verify if the retardance of the SAR assembly matches the design to within the tolerance of  0.01 waves thickness error in each of the pairs of crystal plates. 

Pass Criteria Retardance of each pair of crystal plates shall be 0.01 waves of the design retardance measured at 633.443 nm and 22° Celsius  

Notes

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3.3.11 Modulator: Retardance Uniformity

Type Test Requirement 3.1.1.6-0140, 3.1.1.6-0100-01, 3.1.1.6-0100-02, 3.1.1.6-0100-03, 3.1.1-0270 Preconditions PCM optic assembled  

PCM optic in final cell 

PCM optic in rotary stage in order to automate uniformity measurements 

Test Steps Tests steps laid out in Section 0 explains how the modulation efficiency and retardance is determined for any given location on the clear aperture for the normal incidence case.  

Map modulation efficiency at a minimum of 5 locations evenly distributed over the clear aperture. If the modulation efficiency meets the requirement then retardance uniformity is also confirmed.  

Pass Criteria Retardance uniformity across the aperture of the PCM assembly shows that the net retardance of the pairs of plates are within  0.01 waves across the aperture of the PCM assembly 

Average efficiency for the modulator in the design wavelength range shall be greater than 90% of the theoretical maximum for a balanced Q, U and V polarimeter when used in continuous rotation with 10 states evenly sampled per half‐rotation of the modulator. The minimum efficiency for any wavelength within the range of the modulator shall be greater than 80% of the theoretical maximum, 0.46. 

Notes If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm.

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3.3.12 Calibration Retarders: Retardance Uniformity

Type Test Requirement 3.1.1.3‐0144, 3.1.1.3‐0135‐01, 3.1.1.3‐0135‐02, 3.1.1.3‐0135‐03, 3.1.1.3‐0135‐04

Preconditions SAR optic assembled 

SAR optic in final cell 

SAR optic in rotary stage in order to automate uniformity measurements  

Test Steps Tests steps laid out in Section 0 explains how the retardance properties are determined for any given location on the clear aperture for the normal incidence case.  

Map retarder properties at a minimum of 5 locations evenly distributed over the clear aperture.  

Pass Criteria Retardance uniformity across the aperture of the SAR assembly shows that the net retardance of the pairs of plates are within  0.01 waves across the aperture of the SAR assembly 

Notes  If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm.

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4. CALIBRATION LINEAR POLARIZER ACCEPTANCE TESTING

Upon delivery of the WGP from the vendor, the PA&C team will perform the following tests using the NLSP in the lab at NSO, Boulder. The requirement covered by these tests are also indicated below.

4.1 OVERVIEW

Upon delivery of the optic from Moxtek, a complete set of acceptance tests will be performed using the NLSP (see TN-0231) in the lab at NSO, Boulder. The following is a list of tests that will be performed and the requirements they cover.

4.2 ENVIRONMENT

NSO measurements are performed in the NSO Boulder Lab, N130. Modular clean room, class 100,000. Measurements made with the NLSP visible spectrograph are binned to 660 wavelengths from 380 nm to 1100 nm, and the NLSP IR spectrograph are binned to 255 wavelengths from 900 nm to 1650 nm.

4.3 TESTS

Tests described below are performed by NSO and Moxtek. Unless explicitly stated the measurements are performed by NSO.

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4.3.1 Calibration Linear Polarizer: Wavelength Range

Type Test Requirement 3.1.1.3‐0041, 3.1.1‐0220, 3.1.1.3‐0130 Preconditions Linear polarizer procured and mounted in cell 

Test Steps Measure the contrast ratio with Avantes Visible and IR spectrographs 

Plot the contrast ratio as a function of wavelength 

Pass Criteria Shall span the operating wavelength ranges for first  from 380 nm to 5000 nm. 

Contrast ratio is >250:1  

Notes VTF operation wavelength range is 520nm to 870nm (Goal 500nm to 900nm). 

ViSP operation wavelength range is 380nm to 900nm (Goal 380nm to 1600nm).

DL‐NIRSP operation wavelength range is 900nm to 2500nm (Goal 500nm to 

2500nm). 

Cryo‐NIRSP operation wavelength range is 1000nm to 5000nm (Goal 500nm to 

5000nm). 

If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow 

us to perform measurements out to 1600 nm. 

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4.3.2 Calibration Linear Polarizer: Transmission

Type Test Requirement 3.1.1.3-0105 Preconditions Linear polarizer procured and mounted in cell 

Test Steps NSO will measure the transmission with NLSP from 380nm to 1600nm 

1600nm to 5000nm will require another spectrometer. 

Pass Criteria The calibration linear polarizer transmission for 100% linear polarized input aligned with the fast axis of the polarizer shall exceed or meet values as follows. Linear interpolation shall apply between listed wavelengths except for the OH band. Reflectivity shall be consistent with that of a bare aluminum coated optic. 

Wavelength  Requirement Goal 380nm 0.75 0.85 500nm 0.75 0.85 1000nm 0.75 0.85 2000nm 0.75 0.85 3000nm 0.50 0.85 4000nm 0.10 0.85 5000nm 0.00 0.85

 

Notes If NLSP dual spectrograph upgrade is complete, an IR spectrometer will allow us to perform measurements out to 1600 nm.

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4.3.3 Calibration Linear Polarizer: Aperture

Type Inspection Requirement 3.1.1.3-0100 Preconditions Linear polarizer procured and mounted in cell 

Test Steps Visual inspection of the clear aperture. 

Pass Criteria Clear aperture must be at least 110.64mm 

No significant cosmetic damage within the clear aperture  

Contrast ratio must be >250:1 

Notes NSO will measure Contrast Ratio for at least five locations across the clear aperture.

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4.3.4 Calibration Linear Polarizer: Optical Polish

Type Test Requirement 3.1.1.3-0052 Preconditions Polarizer procured  

Test Steps Vender inspection 

Pass Criteria The optical quality of the polarization calibration optic exterior surfaces shall be 20/10 per MIL‐C‐48497A 

Notes

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4.3.5 Calibration Linear Polarizer: Transmitted WFE

Type Test Requirement 3.1.1.3-0080 Preconditions Polarizer procured 

Test Steps Test performed by vendor 

Pass Criteria TWFE shall be less than 3 waves P‐V at 633 nm tip/tilt removed 

Notes

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4.3.6 Calibration Linear Polarizer: Beam Deflection Angle

Type Test Requirement 3.1.1.3-0050 Preconditions Polarizer procured 

Test Steps Test performed by vendor 

Pass Criteria Beam deflection shall be <96 arc seconds 

Notes