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	State Key Laboratory of Applied Optics, University of Chinese Academy of Sciences
Analysis	Full AI Review Included

Technical Documentation & Analysis: MPCVD Diamond for Ultra-Precision Optics

This document analyzes the research paper “Analysis and Prediction of Image Quality Degradation Caused by Diffraction of Infrared Optical System Turning Marks” and connects its findings directly to the superior material solutions offered by 6CCVD.

Executive Summary

The research quantifies a critical manufacturing challenge: the degradation of image quality (MTF) in infrared (IR) optical systems due to residual annular turning marks left by Single-Point Diamond Turning (SPDT) on materials like Germanium, Silicon, and Aluminum.

Problem Quantified: Turning marks diffraction contributes approximately one-third of the total measured MTF decrease in the tested mid-wave IR system.
Solution Proposed: A fast, scalar-based Turning Marks MTF (TMTF) algorithm is developed to predict this worst-case degradation, allowing tolerances to be integrated into the optical design phase.
Computational Efficiency: The TMTF algorithm is validated to be hundreds of times faster than rigorous coupled wave analysis (RCWA), with a relative error in diffraction efficiency of only < 3%.
Material Limitations Highlighted: The paper implicitly confirms that traditional IR materials (Ge, Si, Al) require extensive, time-consuming post-machining polishing (up to a day for a $\Phi$100 mm mirror) to remove diffraction-inducing marks.
6CCVD Value Proposition: MPCVD diamond (SCD/PCD) offers inherent material properties (extreme hardness, low scatter, high polishability) that minimize or eliminate the need for costly, time-intensive post-machining mark removal, ensuring superior optical performance from the outset.

Technical Specifications

The following hard data points were extracted from the analysis of the TMTF algorithm and the tested optical systems (Mid-Wave IR refractive system and metal-based reflective system).

Parameter	Value	Unit	Context
TMTF Computational Speed	Hundreds of times	Faster	Compared to RCWA algorithm
TMTF Diffraction Efficiency Error	< 3%	Relative Error	Accuracy validation against RCWA
Maximum MTF Deviation (TMTF vs. RCWA)	0.033	Absolute Error	Observed at low spatial frequencies
Mid-Wave IR Spectral Band	3.7 to 4.8	µm	Operating range of tested refractive system
SPDT Feed Rate (Aluminum)	2 to 3	µm	Typical machining parameter
SPDT Feed Rate (Germanium/Silicon)	0.5 to 1	µm	Typical machining parameter
Tool Head Radius (Tested Systems)	1	mm	Radius (R) used in h_max calculation
Theoretical Residual Height (h_max)	0.125	nm	Calculated for 1 µm feed rate, 1 mm radius
Minimum F-number for TMTF Reliability	> 2	N/A	System aperture constraint for scalar theory
Polishing Time for $\Phi$100 mm Mirror	~1	Day	Required to remove turning marks on traditional materials

Key Methodologies

The TMTF algorithm provides a rapid, scalar-based method for predicting the worst-case image quality degradation caused by SPDT turning marks.

Ideal SPDT Marks Modeling: Annular turning marks are locally approximated as a linear grating on the optical surface, characterized by a phase polynomial $\phi = Cr$, where C is related to the machining feed rate.
Theoretical Residual Height: The maximum distance between contour peaks and valleys ($h_{max}$) is calculated based on the cutting feed amount (F) and the tool tip radius (R) using the formula: $h_{max} = F^{2} / 8R$.
Diffraction Efficiency Calculation: Scalar diffraction theory is applied, modeling the groove profile as a periodic triangle function, to calculate the diffraction efficiency ($\eta_{m}$) for the 0th and $\pm 1$st orders.
Wavefront Aberration Tracing: Ray tracing is performed across the entrance pupil to calculate the wave aberration (OPD) for specified wavelengths and diffraction orders.
Amplitude Spread Function (ASF) Normalization: The ASF is calculated via the Fourier Transform of the complex exponential of the OPD, and then normalized using the calculated diffraction efficiency ($\eta_{m}$) for the corresponding order.
Coherent and Incoherent Summation: ASFs of different diffraction orders at the same wavelength are coherently summed. The resulting monochromatic Point Spread Functions (PSFs) are then incoherently summed across all wavelengths to obtain the multi-wavelength PSF ($PSF_{sum}$).
MTF Derivation: The final Modulation Transfer Function (MTF) is calculated by taking the magnitude of the Fourier Transform of the $PSF_{sum}$.

6CCVD Solutions & Capabilities

The research demonstrates that residual surface roughness (turning marks) is a primary constraint on optical performance, particularly in the IR spectrum. 6CCVD’s MPCVD diamond materials offer a direct solution by providing surfaces that inherently meet or exceed the required roughness tolerances, minimizing or eliminating the need for costly, time-consuming post-machining processes like polishing.

Applicable Materials

Application Requirement	6CCVD Material Recommendation	Rationale
High-Performance IR Lenses/Windows	Optical Grade Single Crystal Diamond (SCD)	SCD is transparent from UV to Far IR, offering superior thermal conductivity and hardness compared to Germanium or Silicon. This minimizes thermal distortion and ensures exceptional surface stability.
Large-Aperture Reflective Optics	Optical Grade Polycrystalline Diamond (PCD)	We offer PCD plates up to 125 mm in diameter, ideal for replicating the inch-size reflective systems tested. PCD provides high stiffness and low scatter, crucial for maintaining image quality.
Low-Scatter, High-Reflectivity Mirrors	Polished SCD/PCD with Custom Metalization	Diamond surfaces can be polished to Ra < 1 nm (SCD) or Ra < 5 nm (PCD). This ultra-low roughness inherently suppresses the diffraction effects analyzed by the TMTF algorithm.
Electro-Optical/BDD Applications	Boron-Doped Diamond (BDD)	For applications requiring conductive substrates or electrodes integrated into the optical system, BDD offers the necessary electrical properties alongside diamond’s optical and mechanical benefits.

Customization Potential

The paper highlights the need for precise control over surface geometry and material integration. 6CCVD provides comprehensive customization capabilities to meet these demands:

Custom Dimensions: We supply plates and wafers up to 125 mm (PCD) and custom substrates up to 10 mm thick, accommodating the large-aperture systems discussed in the research (e.g., 76.6 mm entrance pupil diameter).
Ultra-Low Roughness Polishing: Our internal polishing capability achieves surface roughness of Ra < 1 nm for SCD and Ra < 5 nm for inch-size PCD. This level of finish is critical for suppressing the high-order diffraction light caused by turning marks ($h_{max}$ is typically in the sub-nanometer range).
Integrated Metalization: For reflective optics, such as the metal-based mirror system analyzed, 6CCVD offers in-house deposition of standard and custom metal layers, including Au, Pt, Pd, Ti, W, and Cu, ensuring robust, low-scatter reflective coatings directly on the diamond substrate.

Engineering Support

The TMTF algorithm allows engineers to incorporate diffraction-induced tolerances into the design phase. 6CCVD’s in-house PhD team specializes in material science and optical engineering and can assist with:

Material Selection: Guiding the transition from traditional IR materials (Ge, Si) to diamond to maximize thermal, mechanical, and optical performance.
Tolerance Optimization: Assisting in defining surface roughness specifications for similar Infrared Optical System projects to ensure that the final product meets MTF requirements without excessive, costly post-processing.
Custom Recipe Development: Providing materials tailored to specific SPDT or post-processing requirements, leveraging diamond’s superior hardness and stability.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. Global shipping (DDU default, DDP available) ensures rapid delivery worldwide.

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]