Point Source Transmittance

Point Source Transmittance (PST) is one of the most widely used metrics for quantifying stray light performance in optical systems. It provides a system-level measure of how much light from an off-axis point source reaches the detector, enabling engineers to evaluate and optimize stray light suppression.

PST is particularly critical in applications such as space telescopes, remote sensing systems, and low-signal imaging, where even small levels of stray light can significantly degrade performance.

Prerequisites:

Speos 25R2 (Premium or Enterprise for GPU raytracing) or later version
Python 3.10 with the following packages installed: win32, os, rich (optional)

Important notice: The script listed is available in the attachments of this article. It includes separate folders with their corresponding names and are provided under the MIT License, included also in the results and example data.

Authored by TJ Gilleran, Noah Hamstra, Laura Martin Jimenez, Tobias Lauinger

download example (.zip)

Point Source Transmittance Defined

Point Source Transmittance describes the ratio of transmitted irradiance at the detector to the incident irradiance from a point source located at a specified off-axis angle.

Key Concepts

PST characterizes the system response to external illumination
It is typically evaluated as a function of off-axis angle
Results are often plotted on a log scale

PST curves show:

Scattering from internal surfaces
Specular reflections (glints)
Higher-order stray light paths

Why PST Matters

Stray light is defined as optical energy reaching the detector that does not follow the intended imaging path and can reduce contrast and measurement accuracy.

PST provides a direct metric to:

Quantify off-axis light rejection
Compare design alternatives
Validate system performance against requirements
Identify dominant stray light mechanisms

In many optical systems, PST is used as a primary merit function for evaluating stray light suppression performance.

Point Source Transmittance Interpretation

Point Source Transmittance (PST) is traditionally defined as the ratio of stray-light irradiance reaching the detector to the irradiance entering the optical system from an off-axis source at angle θ. In Stray Light Analysis and Control [1], Eric Fest defines PST as:

$${PST}=\frac{{E}_{SL}}{{E}_{inc}}$$

where:

${E}_{SL}$ is the stray-light irradiance at the focal plane (detector)
${E}_{inc}$ is the irradiance entering the system aperture from a collimated source

This definition compares irradiance at two different locations in the optical system: the entrance aperture and the detector.

For practical PST analysis, it is often more convenient to normalize detector irradiance to the detector response for an on-axis source. In that case PST is calculated as:

$${PST}(\theta)=\frac{{E}_{detector}(\theta)}{{E}_{inc}(\theta_{0})}$$

where:

${E}_{detector}(\theta)$ is the irradiance measured at the detector for a source at angle $\theta$
$E_{inc}(\theta_0)$ is the incident irradiance entering the aperture stop from an on-axis ($0^\circ$) source

If transmission losses are small for the on-axis reference case, the irradiance entering the system and the irradiance reaching the detector are approximately proportional:

$$E_{detector}(0) \approx T \cdot E_{inc}(0)$$

where $T$ represents the total system transmission. Under this assumption, using ${E}_{inc}(\theta_{0})$ or $E_{detector}(0)$ as the normalization reference gives nearly identical PST values and does not significantly affect the PST curve shape.

For this reason, many stray-light analyses normalize to the on-axis detector irradiance, yielding the quantity referred to by Eric Fest as Normalized Detector Irradiance (NDI) [1]:

$$NDI(\theta)=\frac{E_{detector}(\theta)}{E_{detector}(0)}$$

The key distinction is that PST normalizes to irradiance entering the optical system, whereas NDI normalizes to irradiance measured at the detector for the on-axis reference source. This script calculates and plots NDI, however, under the assumption of high on-axis transmission efficiency, this approximation closely follows PST behavior.

A PST curve plots:

X-axis: Off-axis angle (degrees)
Y-axis: Transmittance (log scale)

PST curves are commonly used to identify critical scattering surfaces and system weaknesses [2]

Workflow Setup and Analysis of Results

This script automates the data reading, storing, writing and plotting of the point source transmittance curve.

Set up stray light analysis sources using automated and parameterized source input parameters:

Following the steps for the Automated Parametric Surface Source Script outlined in the following article to set the input parameters

Automation Scripts: Stray Light Analysis – Automation Scripts – Ansys Optics
Set Sensor Parameter

Set the sensor parameter to be Radiometric and Layer by Source to capture the source contributions at each sweep angle
Simulation Parameters

Create a new Direct Simulation. Utilize GPU raytracing for quickest results using Speos Premium or Enterprise. The same data can be output using CPU compute with Speos Pro. By using GPU raytracing, the user can dramatically decrease the time to get results. This example traced 10 billion rays in 4 hours on an engineering laptop with Nvidia RTX Pro 5000 Blackwell Generation graphics card. The ray count refers to the total number of rays traced for all sources combined. Simulating fewer sun positions reduces the number of required rays and can therefore decrease the simulation time

Note: Prerequisites for Simulation Setup:

Sweeping from on axis source at 0 degrees to off axis sources up to 90 degrees, with 1 degree resolution (total of 90 layers including on-axis reference flux)
The first source layer in the XMP file corresponds to the on-axis source (reference flux), and subsequent layers correspond to increasing angles off-axis
The script relies on this ordering to correctly normalize the PST values and plot them against angle

Running the Script

Open the downloaded script in the user preferred IDE such as Microsoft Visual Studio
Using the precalculated data, update the path in the script to point to the output *.xmp file
Set “plot” and “csv” to be True. Setting “plot” to True uses the python package matplotlib to generate a plot of the PST. Setting “csv” to True outputs the data to a newly created *.csv file for additional customizable post-processing

Results and Interpretation

Two example PST curves are shown below. Both have been generated using previously defined models available on the Speos Application Gallery.

Example 1: Smartphone Camera

The geometry and optical design exchange file from the following article was used to create this PST curve:

Stray Light Analysis – Smartphone Camera – Ansys Optics

Simulation summary:

GPU raytrace with 10 billion rays in 4 hours and 4 minutes on Nvidia RTX Pro 5000 Blackwell Generation card

Example 2: Ritchey-Chretien Telescope

The geometry and optical design exchange file from the following article was used to create this PST curve:

Stray Light Analysis – Telescope System On-Axis – Ansys Optics

Simulation summary:

GPU raytrace with10 billion rays in 2 hours and 4 minutes on Nvidia RTX Pro 5000 Blackwell Generation card

Discussion

Source positions corresponding to PST inflection points can be simulated on CPU with Light Expert to identify and visualize the critical stray light paths and their geometry interactions. This allows for an easy way to characterize and measure stray light within an optical system as a benchmark for comparing designs and applying additional stray light mitigation techniques