# Compact Numerical Aperture 0.5 Fiber Optic Spectrometer Design Using Active Image Plane Tilt

## TL;DR

This paper introduces a new design method for high numerical aperture fiber optic spectrometers using an image plane tilt to simplify the lens design and improve performance.

## Contribution

A novel method for designing high NA spectrometers by incorporating an active image plane tilt to reduce lens achromatism and aberration demands.

## Key findings

- An NA0.5 spectrometer was successfully designed using four lenses of two materials.
- The spectrometer achieved an MTF above 0.5 with a spectral resolution of 6.5 nm.
- The method reduces the need for complex achromatism in large aperture lens design.

## Abstract

The numerical aperture of the spectrometer is crucial for weak signal detection. The transmission lens-based configuration has more optimization variations, and the grating can work approximately in the Littrow condition; thus, it is easier to acquire high numerical aperture (NA). However, designing a large aperture focusing lens remains challenging, and thus, ultra-high NA spectrometers are still difficult to acquire. In this paper, we propose a method of setting image plane tilt ahead directly when designing the large aperture focusing lens to simplify the high NA spectrometer design. By analyzing the accurate demands of the focusing lens, it can be concluded that a focusing lens with image plane tilt has much weaker demand for achromatism, and other monochromatic aberration can also be reduced, which is helpful to increase the NA. An NA0.5 fiber optic spectrometer design is given to demonstrate the proposed method. The design results show that the NA can achieve 0.5 using four lenses of two materials, and the MTF is higher than 0.5 when the spectral dispersion length is 12.5 mm and the pixel size is 25 μm, and thus, the spectral resolution can achieve 6.5 nm when the spectral sampling ratio is 2:1. The proposed method can provide reference for applications when appropriate materials are limited and high sensitivity is necessary.