1 Introduction

1.1 MTF (Modulation Transfer Function)

Modulation Transfer Function (MTF) is the measurement of a lens’ ability to transfer contrast at a particular resolution from the object to the image. It is the widely accepted fundamental parameter for the characterisation of optical systems worldwide. Knowledge of the MTF curves of the lenses and camera sensors involved in an optical system helps optimise optical system performance.

1.2 Measurement of MTF

With LEO satellites, the image is moving on the surface of the detector, and thus MTF has to be measured dynamically. The CNES (French Space Agency) has built a bench to measure dynamic MTF of detectors (CCD and CMOS), especially those working in TDI (Time delay and integration) mode. It is based on a moving edge, synchronized with the movement of charges inside the TDI detector.

This document details how the MTF of the FINCH Eye Build I will be tested. This test will likely be executed in Spring 2023 and its results shall be compared to our requirement(s) obtained in collaboration with Data Processing.

2 Test Methodology

2.1 Overview

For this test, we are not evaluating MTF at all spatial frequencies. The frequency of interest is the specific Nyquist frequency: $f_N=1/2a$ where a = pixel pitch.

One easy method for the MTF measurement at a defined frequency is the evaluation of the contrast. Here, we use an object made of black & white fringes. At Nyquist frequency, the image of a fringe has the same width as a pixel. The spatial resolution is directly linked to the capacity to distinguish the black from the white.

The image of this object on a pixel as a function of its position is a sine wave, so the Contrast Transfer Function (CTF) is easily calculated as:

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where ϕ_dark = dark signal level

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2.2 Experimental Procedure

  1. An integrating sphere is used as the light source and the object is in the focal plane of the collimation lens, mounted on a 3 axis motorized system.
  2. A mirror is mounted on a rotary stage that will simulate the Earth rotating.
  3. A focalization lens allows the image to be formed on the detector.
  4. For the static measurement, the object is moved step by step following the Y-axis. For every step, the level on the chosen pixel is stored.
  5. For the dynamic measurement, the rotary stage is turning at the defined speed (corresponding to the detector charge transfer).