Analysis and Prediction of Image Quality Degradation Caused by Diffraction of Infrared Optical System Turning Marks

At a Glance

Metadata	Details
Publication Date	2023-08-17
Journal	Photonics
Authors	Haokun Ye, Jianping Zhang, Shangnan Zhao, Mingxin Liu, Xin Zhang
Institutions	Changchun Institute of Optics, Fine Mechanics and Physics, State Key Laboratory of Applied Optics
Analysis	Full AI Review Included

Executive Summary

This research introduces a rapid, high-accuracy algorithm (TMTF) for predicting image quality degradation in infrared optical systems caused by diffraction from Single-Point Diamond Turning (SPDT) marks.

Core Value Proposition: The TMTF algorithm allows engineers to quantitatively predict the worst-case impact of turning marks on the Modulation Transfer Function (MTF) during the optical design phase, enabling the integration of manufacturing tolerances.
Computational Efficiency: TMTF is based on scalar diffraction theory and linear system theory, making it hundreds of times faster than the rigorous Coupled Wave Analysis (RCWA) method, significantly reducing computational resource and time constraints for large-aperture systems.
High Accuracy: The algorithm demonstrates high computational accuracy, with a relative error of only 3% in diffraction efficiency compared to RCWA, and a maximum MTF deviation of 0.033 at low frequencies.
Tolerance Allocation: This method facilitates the quantitative prediction of optical manufacturing tolerances required to meet specific image quality requirements, avoiding costly iterative manufacturing and testing stages.
Practical Impact: In a tested mid-wave infrared refractive system, the MTF decrease attributed solely to turning mark diffraction was approximately one-third of the total MTF decrease observed after final assembly and adjustment.
Applicability Range: The TMTF algorithm provides reliable results for systems with an F-number greater than 2, covering the needs of general infrared optical systems.

Technical Specifications

Parameter	Value	Unit	Context
TMTF Speed Advantage	Hundreds of times faster	N/A	Compared to vector-based RCWA.
TMTF Diffraction Efficiency Error	Max 3% (Relative)	N/A	Compared to RCWA for broadband IR systems.
TMTF MTF Deviation	Max 0.033	N/A	Low frequencies, Metal-based RC system.
RC System PSF Calculation Time (RCWA)	~4 h	Time	For 0, +1, -1 diffraction orders.
RC System PSF Calculation Time (TMTF)	<1 min	Time	For 0, +1, -1 diffraction orders.
RC System Central Wavelength	1550	nm	Ritchey-Chrétien (RC) reflective system.
RC System Feed Rate	2	µm/r	SPDT parameter for RC system.
Refractive System Wavelength Band	3.7 to 4.8	µm	Mid-wave infrared system tested.
Refractive System Effective Focal Length	305	mm	Mid-wave infrared system.
Refractive System Feed Rate	1	µm/r	SPDT parameter for Germanium lens.
TMTF Applicability F-number	> 2	N/A	Systems where the algorithm achieves good results.
Max Deviation (Blaze Grating)	0.0525	N/A	Occurs at the blaze wavelength (4.1 µm).
Incident Angle Range (Reliable)	-40 to 50	°	Range where TMTF and RCWA results are similar.

Key Methodologies

The Turning Marks MTF (TMTF) algorithm integrates SPDT parameters into optical system analysis using a hybrid coherent/incoherent calculation approach:

Turning Mark Modeling:
- The annular turning marks are locally approximated as a linear phase grating structure on the optical surface.
- The theoretical residual height (h_max) is determined by the tool feed rate (F) and tool tip radius (R) using the formula: h_max = F² / 8R.
- The additional phase (φ) introduced by the grating on the incident light is modeled using a phase polynomial (φ = Cr).
Diffraction Efficiency Calculation:
- Diffraction efficiency (η_m) for the m^th order is calculated using scalar diffraction theory, based on the periodic triangle function model of the groove profile.
- Only the -1st, 0th, and +1st diffraction orders are considered, as higher orders have negligible energy.
Wavefront Aberration and ASF Calculation:
- Ray tracing is performed for a grid of rays across the entrance pupil to calculate the wavefront aberration (OPD^m_ω) for the specified wavelength (ω) and diffraction order (m).
- The Amplitude Spread Function (ASF) is calculated by taking the two-dimensional Fourier transform of the complex exponential of the wavefront aberration.
Coherent and Incoherent Summation:
- Normalization: The ASF for each order is normalized by its corresponding diffraction efficiency (η^ω_m).
- Coherent Addition: Normalized ASFs of different orders (m) at the same wavelength (ω) are coherently superimposed to form the coherent ASF (ASF_sum).
- PSF Calculation: The Point Spread Function (PSF) for each wavelength (PSF_ω) is derived from the coherent ASF.
- Incoherent Addition: PSFs from different wavelengths (ω) are incoherently summed to obtain the multi-wavelength PSF (PSF_sum).
MTF Derivation:
- The final MTF is calculated as the magnitude of the Fourier Transform of the total multi-wavelength PSF.

Commercial Applications

This technology is crucial for industries requiring high-performance infrared optics manufactured using ultra-precision techniques.

Defense and Military Systems: Used in the design and manufacturing of high-precision infrared optical systems, including thermal imaging cameras, missile guidance systems, and surveillance optics, where stray light and image fidelity are critical performance metrics.
Aerospace and Astronomy: Applicable to large-aperture reflective systems (like Ritchey-Chrétien telescopes) and space-based sensors that rely on SPDT-machined metal mirrors for lightweight, high-performance operation.
Optical Manufacturing and Metrology: Provides a tool for quality control and process optimization in ultra-precision machining facilities, allowing manufacturers to set precise SPDT parameters (feed rate, tool radius) that meet specified MTF tolerances without excessive post-polishing.
Infrared Sensor Technology: Relevant for systems utilizing mid-wave infrared (MWIR) and long-wave infrared (LWIR) materials (Germanium, Silicon, Zinc Sulfide) where diffraction effects from turning marks are more pronounced due to longer wavelengths.
Cost Reduction and Production Efficiency: By accurately predicting image degradation, the method allows engineers to omit unnecessary polishing steps if the predicted MTF remains acceptable, leading to significant savings in manufacturing time and cost.

View Original Abstract

This paper addresses the issue of reduced image quality due to annular turning marks formed by single-point diamond turning (SPDT) during the processing of metal-based mirrors and infrared lenses. An ideal single-point diamond turning marks diffraction action model to quantitatively analyze the impact of turning marks diffraction on imaging quality degradation is proposed. Based on this model, a fast estimation algorithm for the optical modulation transfer function of the system under turning marks diffraction (TMTF) is proposed. The results show that the TMTF algorithm achieves high computational accuracy, with a relative error of only 3% in diffraction efficiency, while being hundreds of times faster than rigorous coupled wave analysis (RCWA). This method is significant for reducing manufacturing costs and improving production efficiency, as it avoids the problem of being unable to compute large-size optical systems due to computational resource and time constraints.

Tech Support

Original Source

DOI: https://doi.org/10.3390/photonics10080937

References

2017 - Highly efficient machining of non-circular freeform optics using fast tool servo assisted ultra-precision turning [Crossref]
2019 - Tool path generation of ultra-precision diamond turning: A state-of-the-art review [Crossref]
1975 - Residual Surface Roughness of Diamond-Turned Optics [Crossref]
2021 - Diffractive Optical Characteristics of Nanometric Surface Topography Generated by Diamond Turning [Crossref]
2019 - Understanding Diffraction Grating Behavior: Including Conical Diffraction and Rayleigh Anomalies from Transmission Gratings [Crossref]
2022 - Study of diffractive fringes caused by tool marks for fast axis collimators fabricated by precision glass molding [Crossref]
2020 - Diffraction Efficiency Evaluation for Diamond Turning of Harmonic Diffractive Optical Elements [Crossref]
2000 - Simple Estimates for the Effects of Mid-Spatial-Frequency Surface Errors on Image Quality [Crossref]