As promised, here is the first upgrade on the [»] Raman spectrometer that I have presented two months ago.
One of the first things that I wanted to address was the imaging lens limitations. Indeed, with the previous system that was based on two 50 mm doublet achromats, the resolution was limited to about 0.35…1.3 nm which would prevent the spectrometer from doing anything better than 15…30 cm-1. Also, with the multimode laser used, the overall resolution was about 34 cm-1. The experimental resolution tended to worsen at the edge of the spectrum however which was revealed in the 3000 cm-1 region of the spectrum of iso-propanol.
Today, we will fix that issue by increasing the resolution of the spectrometer to 0.2 nm which will ultimately translate to about 5-7 cm-1. Because I am still using the multimode laser, the Raman spectra will however not reach that resolution yet.
Even in the absence of the laser swap, the resolution already improves as can be seen in the new spectrum of iso-propanol shown in Figure 1.
The biggest change with the old spectrum is located in the 3000 cm-1 region where the three peaks are now fully resolved as can be seen in Figure 2. The two peaks on the right are distant by only 19 cm-1 and appear fully resolved from each other.
The ideal resolution of the spectrometer is reached when the FWHM of a peak is 3 pixels large. It is not recommended to go below that threshold or you will run into troubles when trying to discriminates neighbouring peaks later or when trying to fit profiles to peaks. With the camera used, that equals to 10.4 µm which can be achieved using a 10 µm slit and an optics with a PSF FWHM of 7 µm (√(7²+(cos(45.5°)*10)²) = 10.4).
To achieve this PSF I have spent a lot of time optimizing custom lens systems made from stock parts like I did in the [»] custom microscopy objective post. Things were a bit trickier here because the system is not monochromatic. After some effort I managed to produce a 4 lenses objective that could achieve a 7 µm spot width at an input numerical aperture of 0.12. I was quite happy until I introduced this lens into the spectrometer design where the performances dropped to a 16 µm spot! Even by stopping down the system a lot the resolution did not improve…
Since I was clearly not happy with the results, I decided to look for an alternative at machine vision lens manufacturers. I was lucky enough to find the NAVITAR MVL50M23 which fits right into the existing spectrometer setup and was able to deliver a theoretical 7-8 µm spot at f/4. The lens is old at 180€ at Thorlabs or 155€ if you purchase it directly from the manufacturer.
The quick assembly of Figure 3 will allow you to replace the old imaging lens by the machine vision lens. Because there is already a stop inside the lens, you can remove the external aperture in front of the collimation lens.
I also swapped the 20 µm slit by a 15 µm one. I could have ordered a 10 µm slit but for some reason I did not. Maybe I should sleep more at night :)
With a 15 µm slit and a 7-8 µm spot width, the theoretical resolution of the spectrometer should be about 13.2 µm which translated to 3.8 pixels or a 0.2 nm resolution. With the 10 µm slit I could have dreamed of 0.15 nm. Nonetheless, 0.2 nm already achieve very good performances and let more light enter the spectrometer which is always good in Raman spectroscopy.
The resolution was confirmed experimentally with a Neon lamp as shown in Figure 4.
The resolution at 1700 cm-1 is about 6-7 cm-1 as predicted. Note however that at higher wavelengths/wavenumbers, a shoulder appears next to the peak. This was foreseen by the raytracing as shown in the PSF at 640 nm in Figure 5. Later experimentation with actual Raman spectra will show if this is a problem or not.
Before I end this post there is one important thing that I need to stress out: do not substitute the NAVITAR lens by another one.
This needs some explanation.
A lens as used in photography is defined by two important factors: (1) its resolution, (2) its entrance pupil location and diameter. When selecting an objective lens for the spectrometer, I had to be very careful with these.
First, the resolution provided by the lens should be high enough to allow spot sizes of 7 µm or less. The datasheet of the NAVITAR lens reports a 100 lp/mm at centre and 80 lp/mm in the corners. Since the lens was designed for 2/3” sensor and we are using a smaller sensor, we should benefit from a ~5 µm spot size. Don’t overlook resolution, 5 µm is really good performances and you will have to spend several thousands of dollars to get something similar with a DSLR camera. This is due to the fact that SLR cameras have much larger field of views and until recently their pixels were therefore much larger. So don’t try swapping this lens with a cheap DSLR lens, it will not work.
Second is the study of the entrance pupil position and diameter. Previously, the stop was located at the collimation lens. Here, the stop will be located somewhere inside the objective. Because the stop is the position at which the rays pivot into the system, placing the stop away from the grating means that for the same input numerical aperture, a larger portion of the grating and collimation lens will be used. It is very important to be sure that rays do not exceed the physical dimensions of these elements or clipping will occur.
When studying the stop position, you can either work with the stop itself or any of its images in the system. The stop image in front of the lens is called the entrance pupil and the stop at the rear of the lens is called the exit pupil. When assembling systems with several stops, you need to enforce that the exit pupil of the first system matches perfectly the entrance pupil of the second system or clipping (vignetting) will occur.
The problem with most camera lenses is that their entrance pupils are virtual. That is, it lies at the back of the first lens and you cannot physically super-impose an element (such as the grating) on it. That means you should be very careful when putting a camera lens in a system like ours.
Finally, experience also teaches us that it is not because the camera lens achieve a given resolution on its own that it will do when introduced in a system. True resolution will depend on how aberrated the input wavefront reaches the entrance pupil of that lens.
All these things taken together, you should always simulate the complete system to have an idea on how it will behave. And that is precisely where you will run into troubles: you don’t have the prescription data for the lens you would like to integrate. Don’t even think about asking the lenses manufacturers to share this with you as it is trade secrets they build their business on.
In the machine vision world things are a bit fancier because you can eventually ask for what is called a blackbox model of the lens. A blackbox model is a special encrypted file that works with professional lens design software and which allows you to trace rays without having the actual prescription data. It is however very difficult to get these blackbox models for cheap lenses like the one used here and they are usually offered for large volume integration by commercial companies.
That being said, I was extremely lucky here and managed to get the blackbox model for the NAVITAR lens. This is how I manage to assess the actual performances of the system before building it. The system is shown in Figure 6.
The white rectangles are part of the blackbox model and represent group of lenses. You can notice the stop (in orange) located between the blocks. The smaller rectangles are windows that protect the objective and the camera. It is important to include them in the simulation because they will introduce small amount of spherical aberrations that will affect overall resolution.
The system is represented here for an input numerical aperture of 0.12 and you can see that it almost completely fills the 25×25 mm² surface of the grating. It is not recommended to use the full grating surface as edge tend to have more defects which can produce stray light into the system.
That concludes this post on imaging lens and the note I wanted to make on commercial lenses.
Next upgrade is coming soon, so stay tuned for updates![⇈] Top of Page
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