## How to optimize non-sequential optical systems

Category: Product News

The optimization tools in OpticStudio enable users to systematically improve the performance of their design, whether it is a spaces telescope, projector system, or cell phone camera lens. This process requires setting system parameters as variable and defining performance criteria in the Merit Function Editor. These choices can have a huge impact on the design, so it is important to select appropriate variables and criteria. The criteria available differs between Sequential and Non-Sequential modes.

This blog post gives a recommended approach to the optimization of non-sequential optical systems. The recommended methods are to use Pixel Interpolation, aggregate detector data (moment of illumination data), and the orthogonal descent optimizer. As an example, a free-form mirror is optimized to maximize the brightness of an LED from 23 Cd to >250 Cd in just a few steps.

Damped least-squares vs orthogonal descent.

There are two local optimization algorithms in OpticStudio: damped least squares (DLS) and orthogonal descent (OD). DLS uses numerically computed derivatives to determine a direction in solution space which produces a design with a lower merit function. This gradient method has been developed specifically for optical system design and is recommended for all imaging and classical optical optimization problems. In the optimization of pure non-sequential systems, however, DLS is less successful because detection is performed on pixelated detectors; the merit function is inherently discontinuous, and this can cause the gradient method to fail.

Below is a scan of the merit function of a non-sequential system as a function of just one variable.

For long regions of merit function space, there is no change in the merit function at all, and when change does come it is sudden and discontinuous. This makes optimization by gradient search techniques difficult.

Orthogonal Descent optimization uses an orthonormalization of the variables and discrete sampling of solution space to reduce the merit function. The OD algorithm does not compute numerical derivatives of the merit function. For systems with inherently noisy merit functions, such as non-sequential systems, OD will usually outperform DLS optimization. It is very useful in optimization problems like illumination maximization, brightness enhancement, and uniformity optimization.

Pixel interpolation and non-sequential optimization

In addition to the specific algorithm used, OpticStudio contains several features that significantly improve the optimization of non-sequential systems.

As mentioned previously, non-sequential solution space tends to be discontinuous due to the pixelated nature of detectors. If the energy in each ray is assigned to only one pixel, there is no quantitative difference when a system change causes the ray to shift anywhere within that pixel. As a result, optimization is difficult, with discontinuous derivatives in the merit function occurring when a ray crosses the boundary into a new pixel.

This can be illustrated by scanning a single ray across a detector. The universal plot below shows how the irradiance centroid on a detector changes with ray location.

One way to avoid quantization effects due to pixelated detectors is to use pixel interpolation. Instead of 100% of a ray’s energy being assigned to the single pixel struck, a fraction of the energy is apportioned to adjacent pixels based upon the location of the ray intercept inside the pixel. As a result, there is a noticeable change in the merit function as a system change causes a ray to move across a pixel. Pixel interpolation can be enabled in the detector’s Object Properties...Type.

If we scan a ray across a detector with pixel interpolation enabled, the change in irradiance centroid, and most other criteria, is continuous, and DLS can be easily used.

The irradiance centroid reported in the merit function is computed using the NSDD optimization operand. NSDD stands for non-sequential incoherent intensity data and is the most useful operand for reporting incoherent detector data. It enables optimization of several important criteria: minimum spot size (min RMS spatial width), maximum energy (total flux), spatial uniformity (standard deviation of all pixels), collimation (minimum RMS angular width), and more.

For a detailed description of NSDD capabilities, see the OpticStudio Help File section: The Optimize Tab (Sequential UI Mode) >Automatic Optimization Group>Merit Function Editor (automatic optimization group) >Optimization Operands by Category>Non-Sequential Ray Tracing and Detector Operands.

To learn more on how to set up your non-sequential system, OpticStudio merit function, OpticStudio freeform mirror, and optimization, you can access the entirety of this Knowledgebase article here.