Experimental power spectral density analysis for mid- to high-spatial frequency surface error control

Javier Del Hoyo; Heejoo Choi; James H. Burge; Geon-Hee Kim; Dae Wook Kim

doi:10.1364/AO.56.005258

Applied Optics
Vol. 56,
Issue 18,
pp. 5258-5267
(2017)
•https://doi.org/10.1364/AO.56.005258

Experimental power spectral density analysis for mid- to high-spatial frequency surface error control

Javier Del Hoyo, Heejoo Choi, James H. Burge, Geon-Hee Kim, and Dae Wook Kim

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Javier Del Hoyo, Heejoo Choi, James H. Burge, Geon-Hee Kim, and Dae Wook Kim, "Experimental power spectral density analysis for mid- to high-spatial frequency surface error control," Appl. Opt. 56, 5258-5267 (2017)

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Table of Contents Category
- Optical Design and Fabrication
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About this Article
History
- Original Manuscript: March 2, 2017
- Revised Manuscript: May 20, 2017
- Manuscript Accepted: May 24, 2017
- Published: June 19, 2017

Abstract

The control of surface errors as a function of spatial frequency is critical during the fabrication of modern optical systems. A large-scale surface figure error is controlled by a guided removal process, such as computer-controlled optical surfacing. Smaller-scale surface errors are controlled by polishing process parameters. Surface errors of only a few millimeters may degrade the performance of an optical system, causing background noise from scattered light and reducing imaging contrast for large optical systems. Conventionally, the microsurface roughness is often given by the root mean square at a high spatial frequency range, with errors within a $0.5 \times 0.5 mm$ local surface map with $500 \times 500$ pixels. This surface specification is not adequate to fully describe the characteristics for advanced optical systems. The process for controlling and minimizing mid- to high-spatial frequency surface errors with periods of up to $\sim 2 - 3 mm$ was investigated for many optical fabrication conditions using the measured surface power spectral density (PSD) of a finished Zerodur optical surface. Then, the surface PSD was systematically related to various fabrication process parameters, such as the grinding methods, polishing interface materials, and polishing compounds. The retraceable experimental polishing conditions and processes used to produce an optimal optical surface PSD are presented.

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	Grit Size (μm)	Removal Depth (μm)	Pressure (PSI)	Spindle Speed (RPM)
Common Phase	40	$\sim 100$	0.25	60
	25	$\sim 75$	0.25	60
	12	$\sim 50$	0.25	60
9-μm Grit Finish Case	9	$\sim 40$	0.25	60
5-μm Grit Finish Case	5	$\sim 25$	0.25	60

	Grit Size (μm)	Removal Depth (μm)	Pressure (PSI)	Spindle Speed (RPM)
Loose Abrasives (Aluminum Oxide)	25	$\sim 75$	0.3	50
	12	$\sim 45$	0.3	50
	9	$\sim 25$	0.3	50
Bound Abrasives	20	$\sim 70$	0.3	50
(Trizact)	9	$\sim 35$	0.3	50

	Study 1	Study 2	Study 3	Study 4	Study 5
Fine grind finish	5-μm/9-μm loose abrasives	9-μm bound/loose abrasives	5-μm loose abrasives	5-μm loose abrasives	5-μm loose abrasives
Polishing interface material	CP (Conventional Pitch) #64	SP (Synthetic Pitch) #64	CP #73/#64/#55	CP#64	CP #55
			CP #73/#64/#55	SP #64	CP #55
			SP #64/#55	LP-66 (Polyurethane pad)	SP #55
Polishing compound	Opaline	Rhodite-906	Rhodite-906	Opaline Zirox-K	Rhodite-906
				Iron Oxide Rhodite-906	Distilled water^a
Polishing time	1–8 h	1–8 h	Until converging to a final PSD ( $\sim 3 h$ )	Until converging to a final PSD	Until converging to a final PSD ( $\sim 3 h$ )
Results in	Section 4.A	Section 4.B	Section 4.C	Section 4.D	Section 4.E

	Specification
Camera detector resolution	$1599 \times 1199 pixels$
Microscope objective magnification	$2.5 \times$	$10 \times$
Object space pixel size	2.76 μm	0.69 μm
Spatial field of view	$4.4 \times 3.3 mm$	$1.1 \times 0.8 mm$

		Spatial Frequency $f$ $({μm}^{- 1})$ Range
Polishing Compound	Interface Material	$X$ , $Y$
		0.0004–0.0100	0.0100–0.0350	0.0350–0.1000
Rhodite-906	CP	−1.36, −6.68	−1.73, −7.35	−1.84, −7.50
	SP	−1.53, −6.78	−1.57, −6.80	−2.11, −7.57
		0.0004–0.0040	0.0040–0.1000
Zirox-K	CP	−2.27, −8.78	−1.56, −7.23
	SP	−1.91, −7.61	−1.91, −7.61
		0.0004–0.0100	0.0100–0.0350	0.0350–0.1000
Opaline	CP	−1.92, −8.35	−1.81, −8.06	−1.30, −7.32
		0.0004–0.0030	0.0030–0.0300	0.0300–0.1000
Iron Oxide	CP	−2.99, −10.98	−1.77, −8.27	−0.95, −6.99
	SP	−2.87, −10.60	−1.98, −8.36	−0.90, −6.87

		Spatial Frequency $f$ $({μm}^{- 1})$ Range
Abrasive	Fit Const.	0.0004–0.0336	0.0336–0.0668	0.0668–0.1000
5 μm, Loose^a	$k^{'}$	1.98	1.71	1.56
	$ϵ_{0}$	2.66	1.55	1.34
	$ϵ_{ini}$	184.00	199.70	128.30
9 μm, Loose^a	$k^{'}$	1.07	1.05	1.01
	$ϵ_{0}$	2.27	1.46	1.28
	$ϵ_{ini}$	54.39	73.49	54.70
9 μm, Bound^b	$k^{'}$	0.8272	0.8216	0.8424
	$ϵ_{0}$	5.98	2.04	0.93
	$ϵ_{ini}$	264.60	215.20	148.80
9 μm, Loose^b	$k^{'}$	1.01	0.93	0.93
	$ϵ_{0}$	6.62	2.91	2.05
	$ϵ_{ini}$	411.70	414.10	267.90

Abstract

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Applied Optics