Toroidal Mirrors for Astigmatism Compensation in Folded Spectrometers
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Solution Overview
Problem
Spectrometers using spherical mirrors in folded configurations suffer from astigmatism, leading to image blurring and reduced sensitivity due to differing focal lengths in tangential and sagittal planes, which current designs attempt to mitigate by minimizing fold angles at the cost of increased complexity and size.
Innovation Solution
Employing specially shaped mirrors, such as toroidal mirrors, to equalize focal lengths in both planes by adjusting their radii of curvature, thereby compensating for astigmatism and optimizing image quality without increasing system complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Volume of moving object
If spherical mirrors are used in a folded configuration, then the optical path can be folded to achieve compact design, but astigmatism is introduced causing image blurring and reduced sensitivity
Solution Approach 1:
The patent applies this principle by using a toroidal mirror surface instead of a spherical one. The toroidal surface has different radii of curvature in the tangential and sagittal planes, allowing independent control of focal lengths in both planes. This enables the mirror to focus light properly in both directions while maintaining the folded optical path configuration, thereby eliminating astigmatism without increasing the spectrometer size.
2Manufacturing precision
If fold angles are minimized to reduce astigmatism, then image quality improves, but the size and complexity of the spectrometer design increases
Solution Approach 1:
The patent applies this principle by changing the geometric parameters of the mirror surface from spherical to toroidal. Specifically, the mirror is designed with different radii of curvature (Rt and Rs) in the tangential and sagittal planes, respectively. This parameter change allows the system to maintain sharp focus in both planes regardless of the fold angle, enabling optimal image quality while preserving a compact folded configuration without increasing design complexity.
3Manufacturing precision
If a toroidal mirror is used to compensate astigmatism, then focal lengths in tangential and sagittal planes are equalized, but the mirror fabrication becomes more difficult
Solution Approach 1:
The patent applies this principle by using a toroidal mirror surface instead of a spherical one. The toroidal surface has different radii of curvature in the tangential and sagittal planes, allowing independent control of focal lengths in both planes. This enables the mirror to focus light properly in both directions while maintaining the folded optical path configuration, thereby eliminating astigmatism without increasing the spectrometer size.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach effectively cancels astigmatism across the spectrometer system, maintaining overall magnification and improving image clarity and sensitivity by ensuring the sagittal and tangential image planes coincide, even with limited detector sizes.
Implementation Method 1
The optical system of a spectrometer projects the image of an illuminated slit onto a plane containing a detector. The formation of the image is governed by the usual issues of magnification and vignetting found in any optical system.
Implementation Method 2
To optimize resolution the width of the slit is focused, which is normally in the tangential plane of the system. The sagittal image comes to a focus behind the detector plane if left uncompensated
Data Source
AI summary
A method of making specially shaped mirrors for astigmatism correction in spectrometers having a folded optical path using two mirrors by determining the curvature of one or both mirrors in the vertical direction such that the focal length in the sagittal direction of each of said one or both mirrors becomes the same as the focal length in the tangential direction wherein the radius of curvature of each of one or both mirror in the sagittal plane is adjusted to be equal to the radius of curvature in the tangential plane of each of one or both mirrors times the square of the cosign of the angle of incidence of the optical path at each of one or both mirrors is described.