Design and evaluation of a spectrometer using off-of-shelf optical components by means of Zemax OpticStudio  optical design sotware

A comparison of multiple Spectrometer Design 

Spectrometers are optical tools to measure the spectral composition of a beam of light. Key features of an optimal spectrometer are: cost, variation of the spot size along the spectral range, spot size compared to the diffraction limit, and minimum presence of aberrations. Here, we present different optical designs to focus the light emerging from a diffraction grating 

Principle of a Spectrometer

As previously mentioned, a spectrometer decomposes the spectral spectrum of a broadband light source. The working principle of a spectrometer can be summarized by: a broadband light source enters the optical system (e.g., spectrometer). The optical system separates the light into individual rays with particular wavelength bands. Those rays are then refocused using a mirror or focusing lens based on the wavelength. Finally, the irradiance of each ray is measured using a photodetector such as a CMOS sensor. Please note that this is quite an oversimplification, and a working spectrometer requires much more design consideration and optimization 

Applications of a Spectrometer

Spectrometers have many different scientific applications including remote sensing, astronomy and medical imaging. For example, remote sensing is used to analyze objects or phenomena using a sensor at high altitudes. Typically, the sensor is mounted on aircraft or satellite. Spectrometers are used to large-scale collection of spectral data. A particular example, the light reflected by objects from sunlight illumination can be recorded by a spectrometer, enabling the measuring of reflectivity data based on object. Such data can be used for applications such as agricultural health monitoring, precision agriculture, wildlife health monitoring, and economic mapping.

Spectrometer Design

To implement a spectrometer, we need to specify the number of spectral channels of our spectrometer. The spectral channels characterizes that spectrometer’s ability to distinguish between wavelength intervals. For example, let us consider a broadband sources with desired spectral samples at wavelengths 𝜆1, 𝜆2, …, 𝜆n. A higher value of n would yield a higher number of channels, enabling a better discrimination of the spectral decomposition. A typically RGB image is sampled at 3 bands. Human eye samples spectral information at 3 bands (known as S, M and L bands) that are not evenly distributed from the visible range (400-700 nm). Typically, we mention: a monochromatic spectral signal if there is a single channel, a multispectral signal if there are between 3-15 spectral channels, and hyperspectral signal should have more than 100 spectral channels. Note that more spectral channels may not be useful for all applications; spectral channels should be selected based on the application’s requirements. For our spectrometer design, we will consider only three spectral channels: 855 nm, 880 nm, and 905 nm. Other design consideration is the spectral resolution of our spectrometer. The spectral resolution is defined as the minimum spectral separation between two spectral channels so they can be distinguished as separable wavelengths from our spectrometer. Typically, the higher the spectral resolution, the higher of spectral channels, leading to hyperspectral imaging 





Design components

A spectrometer is composed of a collimating lens (e.g., collimator), a diffraction grating, a focusing lens, and a detector. Without any loss of generality, we only focused on the optical design of the spectrometer, neglecting the detector in this research undergraduate experience. The collimator lens collects the light emerging from a point source with broadband spectrum and collimates it into a plane wave (e.g., parallel rays). Considering geometrical optics, the point source should be placed at the front focal plane of the collimator lens. In order words, the distance between the point source and the collimator lens is the focal length. The collimator lens controls the beam of rays before the diffraction grating.



After the collimator lens, there is the diffraction grating. The diffraction grating is the core element of a spectrometer since it diffracts light based on the wavelength. The angle of the diffracted rays (β) depends on the wavelength (λ) as β = sin-1[(λ/d)-sin(α)], being d the separation between the slits composing the diffraction grating, and α is the angle of incidence. SimpliBecause the diffraction grating is illuminated by a plane wave, the angle of incidence for all rays is the same independently of the wavelength. Without any loss of generality, we let β = α for the central wavelength (λ0 = 880 nm), setting the diffraction grating at an incident angle of α = sin-1[λ0/(2d)].



The focusing lens takes diffracted light from the diffraction grating and focuses it at its back focal plane. Therefore, the detector’s sensor should be placed at a distance equal to the focal length from the focusing lens. The detector’s size (L) is determined based on three parameters: the spectrometer bandwidth (Δ𝜆 = 𝜆max - 𝜆min, spectral range), focal length of the focusing lens (ff), and diffraction angles of the maximum and minimum wavelegths (e.g., maximum and minimum diffraction angles). In other words, the detector size is equal to L = ff [tan(𝛽max- 𝛼) + tan(𝛽min- 𝛼)] where α = sin-1[λ0/(2d)] is the incident angle.

While the diffraction grating is the core component in the spectrometer, the focusing lens is the facet of the spectrometer’s overall performance. In this work, we have tested the performance of the same diffraction grating for varying types of collimator and focusing lenses, configurations, and materials.

Table 1. List of off-of-shelf optical components used on the different spectrometer designs 

Design 1: Simple design

Note that the spot sizes for the three wavelength (blue = 855 nm, green = 880 nm, and red = 905 nm) are so much bigger than the diffraction limit (black circle on the spot diagram). We can see that this design is not desirable since the spot size is not wavelength invariant.


Design 2: Two focusing lenses

In this second design, we have added an additional achromat lens into the focusing system (AC254-100-B + ACA254-100-A). The effective focal length of the focusing system has been reduced so that the detector sensor should be placed closer. In particular, it should be 25.7 mm from the last surface of the second focusing lens. If we observe the spot size, the dimensions of the spot sizes have been reduced for the three wavelengths compared to design 1. It is important to notice that most of the light is focused within the Airy disk (e.g., diffraction limit = black circle). This design has some achromatic aberrations. Further optimization can be performend to find the optimal distance/space between the two focusing lenses.


Design 3: Two focusing lenses but increased wavelength range (730-870 nm)

The distance between both lenses has been manually adjusted to optimize/reduce the spot size for the three different wavelengths. Overall, most of the spot size converges within the diffraction limit.


Design 4: Three focusing lenses 

In this last design, we do not use any achromat lens since we do not care about the achromatic aberration. This design implements singlet lenses, which are known as low-cost lenses. The first two lenses have lower radius of curvature, leading to less aberrations. Typically, the higher the curvature, the higher the amount of aberrations. Therefore, the third lens on this design aims to reduce the field of curvature. We can realize from the spot diagram that the spot sizes are similar to the first design in which we only used a single lens.

Nonetheless, this design allows us a lot of optimization. For example, one can optimize the space between the three focusing lenses. This optimization adds some vignetting effect for the extreme wavelengths, but the spot size is closer to the diffraction limit. More than 70% irradiance of the spot focus is concentrated within the Airy disk for the three wavelengths.

In this optimized design, there is significant space between the diffraction grating and the first focusing lens, so having the lens further away improves the spot diagram. So, we can reduce the distance between the diffraction grating and the first focusing lens and add some additional space between the other two focusing lenses. With this last optimization, the spot sizes for the three wavelength is slightly smaller than the Airy disk.

Conclusions

Dowloads : Download the different files for the spectrometer click here


Funding: This research undergraduate experience is part of the NSF CAREER award (grant number 2042563)

Credits: The spectrometer experience is implemented using the Global Academic Program (e.g., free license for academia) of Zemax OpticStudio version 22.2.2

Support Contact: Andrej Antic [aantic1@memphis.edu]

                                            Ryan Williamson [rwllmsn8@memphis.edu]

                                   Ana Doblas [adoblas@memphis.edu]