In this article we demonstrate the design of linearly variable optical filters (LVOF) utilized in the design of a portable (mini) spectrometer. The spatially varied spectral response of graded optical filters allows them to isolate different spectral components of input light along one dimension. In this way, variable optical filters can enhance the spectral imaging at the detection plane of the spectrometers by cutting off unwanted wavelengths and stray light. Variable optical filters are also more compact than other angle-based dispersion components used in spectrometers. In the presented workflow, Stack Optical Solver is used for the simulation of the optical filter. The calculated optical properties of the filter are then imported to Ansys Zemax OpticStudio as .json files for further validation and implementation in a mini spectrometer configuration to test its performance.
[[NOTE:]] Lumerical 2023 R1.0 edition and Ansys Zemax OpticStudio 2024 R1.02 editions are required for this workflow.
Overview
Understand the simulation workflow and key results
The workflow presented here relies on segmenting the LVOF across one dimension, where each segment is simulated separately, featuring different thickness and optical properties. The thickness of the filter varies linearly, allowing different wavelengths to pass through the filter along one axis. The filter is divided into nine segments in both Stack Optical Solver and Ansys Zemax OpticStudio simulations, and the exchange of the optical properties in .json format is done using the Lumerical's sub-wavelength model . LVOFs allow devices such as optical spectrometers to isolate different wavelengths of incident light along one dimension. Therefore, unwanted wavelengths and stray light are eliminated. At the same time, they are more compact than other angle-based dispersion components used in spectrometers, e.g. diffraction gratings, renders them as a necessary component of mini spectrometers. The workflow consists of three steps. Step 1 simulates multiple segments of the LVOF with Stack Optical Solver , for each segment the thickness of the layers is increasing linearly. The optical properties of every segment are calculated for normal and oblique incidence and exported as a .json file. Then, in step 2 we construct the LVOF in Ansys Zemax OpticStudio, where each segment is positioned according to the filter’s total lateral size, and validates its functionality. Finally, in step 3, the optical filter is placed before the detection plane inside the mini spectrometer to enhance its performance.
Run and Results
Instructions for running the model and discussion of key results
Step 1: Calculate the transmission data of the LVOF in Ansys STACK
- Open the script file [[stackrt_transmission.lsf]] and run the script. It identifies the maximum transmission wavelength Λ of each segment and creates the .json file with the name: segment_peak ”Λ” nm.
- Locate the nine .json files and copy them in the folder Zemax>DLL>Diffractive.
First, we design the LVOF [1-3]. It is made of consecutive thin films of alternating high (green) and low (yellow) refractive index layers, as indicated below. We discretize the LVOF in 9 segments of fixed thickness. Our example uses 24 layers. A schematic of the filter (not in scale) is given below:
We calculate the transmission of each segment for normal and oblique normal incidence using the Ansys STACK solver due to its efficiency in simulating multilayer films. The dataset is saved in a .json file format, that will later be imported to Ansys OpticStudio. RCWA could alternatively be used for the simulation of periodic structures, as mentioned in the Appendix. The solver of choice depends on the shape of the structure, material, and source as well as the number of frequency points required. The structure consists of high index (2.15) and low index (1.45) non-dispersive layers and a glass substrate. To enhance the spectral response and obtain sharper transmission curves, the structure features a break of periodicity around the middle layer. The transmission curves are presented below for normal incidence for all of the 9 simulated segments. The transmission window of each segment is red-shifted, as the thickness of each layer increases.
Next, the Lumerical script constructs the transmission spectra and the angle dependent response for each segment. The transmission spectra from 530 nm up to 630 nm from normal up to 20 degrees incident light are presented below for segments 1, 5 and 9.
As we can see the spectral position of the transmission peaks are weakly dependent on the angle theta. Segments 1 and 9 support a second mode that is limiting the bandwidth of the LVOF and defining the free spectral range (FSR) of the filter. Furthermore, the script calculates the transmission spectrum of each segment, for normal incidence and performs a validation test of the .json format files.
Step 2: Validate the LVOF in OpticStudio
- Open the Ansys Zemax OpticStudio simulation file [[graded_filter_validation.zmx.zar]] and inspect the NSQ model.
- Define the wavelength of the array source.
- Analyze> Ray trace> Clear & Trace and observe the detector viewer.
This step is an intermediate step between the filter design (step 1) and the spectrometer design (step 3). Since the spectrometer model is quite complex, we design this intermediate step in order to validate the response of the filter based on the created .json files of step 1. In the non-sequential mode of Ansys Zemax OpticStudio, we load the respective .json file – that was produced in the previous step – to the respective object (from 2 to 10), as shown below. We then proceed to validate the response of the assembled filter. The simple optical system in this step consists of an array of nine sources, nine user defined objects (one for each segment) and a color detector. Enabling the stochastic mode will allow for better visualization of the rays of the NSC Shaded Model.
In the Zemax file the segments are brought together and the LVOF is constructed. The segments are modelled using the user defined objects and each segment corresponds to a different object.
The validation of the graded filter is demonstrated here by following two approaches.
In the first approach, every segment of the filter is illuminated by a single wavelength source. To do so, set the An array of 9 sources with the same wavelength is placed prior to the filter with 9 segments. The wavelengths are chosen based on the optical filter transmission peaks recorded in the previous step and can be viewed from the "Wavelength Data". The wavelengths are recorded for the green- yellow-red colors and the bandwidth of the filter is from 537 nm up to 606 nm. The total power and peak illuminance recorded for each wavelength by the detector depends on the segment they are transmitted through Nine ray tracing simulations can be performed separately, one for each wavelength. We Analyze> Ray trace> Clear & Trace for each selected wavelength.
The images below show how the wavelength can be set for each simulation (top image), the NSC shaded model for single wavelength illumination at 569 nm (bottom left), and the detector viewer for every individual wavelength (bottom right).
In the second approach, every segment of the filter is illuminated by a broadband source. In this case, the spectral component passing through each segment collapses to a narrowband spectral range, as defined from the Transmission spectrum of each segment, in step 1. We now activate the wavelengths 1-9 from the wavelength tab and sort them, to perform the broadband simulation. We Analyze> Ray trace> Clear & Trace once and observe the detector viewer.
The wavelengths are set as shown below (top image). The NSC shaded model should look like the image below (bottom left), while the detector viewer is expected to show the respective result (bottom right).
After validating the filter's performance following the approaches described above, the users can now proceed to the final step of the workflow.
Step 3: Simulate the mini spectrometer in OpticStudio and obtain the spectral pattern at the detector
- Open the Zemax project file simulation named mini_spectrometer_nonseq.zprj and inspect the design of the spectrometer with the LVOF filter present.
- Analyze> Ray trace> Clear & Trace for a uniform power spectrum and observe the spectral pattern at the detector.
Α traditional mini spectrometer is designed based on the Czerny-Turner configuration using Ansys Zemax OpticStudio. The spectrometer consists of 2 concave mirrors with 100mm and 70mm radius of curvature each, a reflective diffraction grating (reflective DG) with 1200 lines/mm and the designed variable filter from step 1. The light is launched to the spectrometer through a fiber of 0.15 NA. The detector is placed after the filter to capture all wavelengths that pass through it. The detector has dimensions of 5.6mm×4.2mm and a 12MP resolution, resembling a typical CMOS image sensor. The spectrometer was initially designed in sequential mode and then converted to non-sequential. The total size of the spectrometer in this example is approximately 50mm×50mm. The role of the LVOF is to enhance the signal-to-noise ratio and cut off any stray light. The LVOF is constructed in a similar manner as in step 2 using the subwavelength model. It is placed in front of the detector, as shown in the layout images below.
The total size of the filter and the position of each segment are defined in such a way that the rays of each wavelength are incident mainly to their corresponding segment. The ray tracing simulation is performed with the "Use of polarization" option enabled for the Ray Trace control panel. The distribution and size of the nine images are based on the configuration of the optical setup of the spectrometer and the position of the detector. In this demo, two simulations are performed with different spectrums. The first simulation uses the 9 wavelengths (default setting) as defined in the validation phase of step 2, while the second one uses a uniform spectrum from 536nm to 606nm with 52 wavelength points(go to the non-sequential component editor> Object 2: Source ellipse>properties> sources> Color properties> set source color to: Uniform Power Spectrum , Spectrum: 52 , wavelengths from 0.536 up to 0.606 um.
In the first case (left), the image of every wavelength is displayed on the detector with very high transmission. This was expected since through each segment only the rays of the corresponding peak wavelength are transmitted. From the detector, it can also be observed that the spacing between adjacent images is smaller for less distant adjacent wavelength points. In the second case (right) where 52 wavelengths are used, it can be observed that the images of wavelengths that match the peak transmission of the corresponding segments have the highest transmission values and brightness. The explanation for this observation lies in the number of segments used to construct the LVOF compared to the number of wavelengths used in the system.
The above tests demonstrate the operation of the filter inside the compact spectrometer and how the performance of the device can be enhanced. By default, the mini_spectrometer_nonseq file is set with 9 wavelengths. The wavelengths used by the source can be set from the "Properties→Sources→Source Color", and the wavelengths recorded by the detector can be set from the "Properties→Type→Detector". To conclude, in a scheme where the LVOF is approximated using a very high number of segments, the entire spectrum with very high number of wavelengths can be imaged on the detector with the highest brightness.
Important Model Settings
Description of important objects and settings used in this model
Material choice & geometric features of the multilayer optical filter
Multilayer films support Bragg resonances that are dependent on the refractive index contrast and the accurate film thickness of each deposited layer. Therefore, the spectral selectivity of the filter is sensitive on these design parameters. The model can simulate even non-ideal LVOFs , both in terms of thickness and refractive index contrast with high accuracy, after modifying the refractive index and layer thickness of each layer on the stackrt_transmission.lsf. Furthermore, as stated in [1], increasing the thickness of the films results in higher spectral resolution but a smaller FSR.
Angle of the incident light
As it was seen in step 1, oblique illumination of the LVOF leads to a shift of the transparency window of the film. These design restrictions may relax upon special design of the mini spectrometer components, where the angle of incidence that will impinge on the LVOF can be considered as close to normal incidence. Furthermore, if the LVOF is illuminated differently than normal incidence, we advise users to include simulations with angle steps of at least half degree, so to achieve an accurate interpolation among the different angles.
Detector dimensions
The size of the detector will have a direct impact on the design requirements of the LVOF and the rest of the optical components that will compose the mini spectrometer. More specifically, a larger detector will require a diffraction grating supporting wider diffraction angles, as well as a LVOF with slower varying thickness. A smaller detector, on the other hand will require a steeper change on the thickness of the films.
Taking the model further
Information and tips for users that want to further customize the model.
Other simulation solvers and designs for the LVOF
The presented LVOF design is made from 24 layers. More layers can result in sharper features and stronger wavelength selectivity as stated in [1]. Also, material selection and contrast of the high-low refractive index can improve the filters bandwidth. The bandwidth of the LVOF is limited by the wavelength spacing of the different transmission modes and the free spectral range (FSR). The simulation file of step 1 can be modified to other designs, eg. with structural color filters, extending filter design to other Lumerical solvers such as RCWA or FDTD. Moreover, modification of the LVOF design can be suited for near-infrared spectroscopic applications.
Stray light analysis of the mini spectrometer
Improvements on the design of the mini optical spectrometers may extend to stray light analysis offered by Ansys Zemax OpticStudio. Stray light analysis can be performed to further validate the performance of the spectrometer in terms of optical components surface roughness and scattering. Further optimization of the system depending on the application can be realized through the merit function editor of Ansys Zemax OpticStudio.
Additional Resources
Additional documentation, examples, and training material
Related Publications
- Arvin Emadi, Huaiwen Wu, Ger de Graaf, Peter Enoksson, Jose Higino Correia, and Reinoud Wolffenbuttel, "Linear variable optical filter-based ultraviolet microspectrometer," Appl. Opt. 51, 4308-4315 (2012)
- Nada A. O'Brien, Charles A. Hulse, Donald M. Friedrich, Fred J. Van Milligen, Marc K. von Gunten, Frank Pfeifer, Heinz W. Siesler, "Miniature near-infrared (NIR) spectrometer engine for handheld applications," Proc. SPIE 8374, Next-Generation Spectroscopic Technologies V, 837404 (17 May 2012).
- Tang, H.; Gao, J.; Zhang, J.; Wang, X.; Fu, X. Preparation and Spectrum Characterization of a High Quality Linear Variable Filter. Coatings , Vol. 8 , 308, (2018)