Home/Analysis Technologies/Optical Analysis/Sequential Ray Tracing
Analysis Technologies | Optical Analysis
A method that traces rays on the assumption that they pass through each surface once, in a defined order, and evaluates the performance of imaging and afocal optical systems.
Imaging and afocal systems
Each surface is passed once, in the defined order
Ansys Zemax OpticStudio
What the method is
Rays follow a predefined sequence of surfaces in order, passing through each surface exactly once as they travel from the object plane to the image plane. Systems for which that assumption holds — imaging systems and afocal systems — are what this method addresses.
The model is built as a table of surfaces in sequence. Each surface is given a radius of curvature, a thickness, a material, a semi-diameter and a conic constant, and the spacing of a surface is specified as the distance from the one before it. The system as a whole is expressed not as a set of parts placed in absolute coordinates, but as a chain of local coordinates.
That assumption is also a constraint. Rays that miss a surface, strike the same surface twice, or follow an unintended path cannot be represented in this framework. The dividing line is not whether reflection is present, but whether the order of the surfaces can be assumed. A reflective system such as a telescope can be handled here too, provided the order is fixed.
How it works
The trace proceeds along the predefined sequence of surfaces. Rays travel from the object plane to the image plane, passing through each surface once in the defined order. At each surface, refraction or reflection is applied to update the ray’s position and direction, and optical path length is accumulated across the surface spacings.
The difference in accumulated optical path length — the optical path difference, divided by the wavelength — is the wavefront aberration, defined as the departure of the actual wavefront at the exit pupil from an ideal reference sphere. Expanding the wavefront aberration as a function of field and pupil coordinates yields the classical aberration coefficients. The fourth-order coefficients, that is the first-order aberration coefficients, are given by the Seidel sums. The remaining wavefront error is decomposed into Zernike polynomials and can be read off as terms such as spherical aberration, coma and astigmatism.
What the method is good at
Because a single ray passes through each surface once, the number of intersection calculations is set by the number of surfaces. Large numbers of rays and large numbers of candidate designs can be evaluated in a short time.
By treating the optical path difference as a wavefront aberration and expanding it as a function of field and pupil, design problems can be separated out term by term — spherical aberration, coma, astigmatism and so on.
Surface shapes, spacings and materials are quantities you can vary directly. They connect straight into an optimisation that drives the evaluated quantities towards their targets.
Where it fits
→ When the system is one in which light passes through surfaces in a fixed order — a photographic lens, a telephoto lens, a microscope, a telescope, a relay lens or a spectrometer
→ When evaluating the performance of an afocal system
→ When you want to set the quantities to be evaluated and optimise with the surface data as variables
→ When you want a first, approximate picture of ghost paths arising from double reflection
Systems whose surface order cannot be fixed: systems in which you cannot determine in advance which surface a ray strikes and in what order — prisms, corner cubes, light pipes, geometry imported from CAD — are handled by non-sequential ray tracing. The dividing line is not whether reflection is present, but whether the order can be fixed.
Exhaustive coverage of stray-light paths: a trace that assumes surface order can only give an approximation as far as double reflection. Evaluating paths exhaustively belongs to stray light analysis.
Coherent fields: where the amplitude and phase at intermediate surfaces are themselves required, physical optics propagation is the better fit.
The effect of manufacturing variation: to see the spread of performance against error rather than at nominal values, the work is set up as a tolerance analysis.
Applications
Designing the imaging performance of photographic and telephoto lenses.
Refining the imaging performance of microscopes, telescopes, relay lenses and spectrometers.
Used for the design and aberration correction of eyepiece optics.
Mapping deformation obtained from thermal or structural analysis onto the surfaces and evaluating the resulting change in performance.
Inputs and outputs
INPUT
| Surface data | Radius of curvature, thickness, material, semi-diameter, conic constant |
|---|---|
| System conditions | Aperture, field points, wavelengths |
| Variables | Which surface data the optimisation is allowed to vary |
| Merit function | The set of operands expressing the targets and constraints |
OUTPUT
| Geometric measures | Spot diagrams, and tangential and sagittal ray aberration plots |
|---|---|
| Wavefront | Wavefront aberration expressed as optical path difference |
| Measures that include diffraction | MTF by the FFT and Huygens methods, and the diffraction point spread function |
| Image evaluation | Geometric image simulation, and image simulation including diffraction |
How it is done
Give each surface a radius of curvature, thickness, material and clear aperture, and set the aperture, field and wavelengths.
Mark the surface data to be varied as variables, and build a merit function expressing the targets and constraints.
Run a local optimisation that reduces the merit function, and inspect the converged solution.
Compare spot size, optical path difference and MTF before and after optimisation, and return to the merit function if needed.
How the merit function is built very largely determines the outcome of the optimisation. Step 02 is where most of the time should go.
Comparison with related methods
| Method | Relationship | Main subject | How they divide up |
|---|---|---|---|
| Sequential ray tracing (this method) | This method | Imaging systems whose surface order can be assumed | Traces on the assumption that each surface is passed once and in order, running aberration evaluation and optimisation quickly. |
| Non-sequential ray tracing | Alternative | Systems whose paths are determined by geometry | Intersections are determined solely by the position and properties of the objects and the direction of the ray. A ray may strike the same object any number of times. |
| Physical optics propagation (POP) | Complementary | Propagation of a coherent field | Rays in a spot diagram do not interfere with one another. Where a field in which amplitude and phase interfere is required, this is the method to use. |
| Tolerance analysis | Downstream | The effect of manufacturing variation | Takes the optimised nominal design directly as input and estimates the spread of performance against error, and the resulting yield. |
| Stray light analysis | Downstream | Exhaustive evaluation of unintended paths | A trace that assumes surface order yields only an approximation as far as double reflection. The design is converted, and the work moves on to an evaluation that covers paths exhaustively. |
Available in
Sequential ray tracing is provided as one of this product’s analysis modes. Editing surface data, optimising against a merit function and running a tolerance analysis are all handled in the same environment. See here for licensing, system requirements and adoption.
FAQ
Related technical information
Tell us what you are designing and the characteristics you want to evaluate, and we will suggest the appropriate method and approach.