Spectrophotometry Part #3: SLR Lenses

Recently I had the occasion to fix a few things from the [»] spectrophotometer setup I proposed a few months ago. If you haven’t read the previous yet, I encourage you to do it before proceeding.

In the previous setup, I was using common N-BK7 1” stock lenses to first collimate the light from a 50 µm slit onto a reflective diffraction grating and then imaged the resulting rainbow with a second lens onto a camera sensor. Although I identified that I would get better results using a 6 mm objective as the second lens, I failed to implement the solution. I have now identified that the cause of the problem was the equivalent lens aperture. But rather than just editing the previous post with the fix, I would like to share a few more upgrades I have done on the setup.

The upgraded setup is a bit different because I am now using a transmission grating. It has the same resolution as the one I used previously but I now collect the light from behind the grating rather than by a reflection on the grating. This allowed me to place the second lens much closer to the grating without obstructing the light coming from the collimator. Also, I have now replaced the collimating lens by more accurate lenses. I will come back on this later in this post.

The upgraded setup is shown on Figure 1. As you can see, a lot of parts have been removed from the original setup.  A fiber source directly outputs its light onto a 50 µm slit whose light is collimated using a first lens L1. The light then goes onto the diffraction grating and is collected by a second lens L2. Both lenses have apertures by the natural consequence that they do not extend to infinity.

Apertures play a major role in the setup. Actually, they are the reason why I had issue with the 6 mm lens. The 6 mm imaging objective is a complex combination of lenses that are arranged to achieve less chromatic aberrations than a stock lens of equivalent focal length. Any objective like this one can be idealized as a single lens with little aberrations and an aperture in front of it. My 6 mm objective has a maximum aperture of f/1.4, that is about 4.3 mm. The problem is that the equivalent apertured lens is located at the equivalent focal plane from the camera sensor and not in front of the objective. So even if you have the front part of the objective in contact with the grating, there is still some empty space between the grating and the equivalent apertured lens that is merely located at the back of the objective.

And because the aperture is quite small, most of the rainbow emerging from the grating will be cut before reaching the camera sensor. This situation is represented on Figure 1.

From the physical dimension of the objective I am using, I can infer that the actual cone of light that may reach the sensor is only about 10° which corresponds to a ~100 nm span on a 1200 lines/mm grating. So no matter what, with that particular objective I will not be able to reach the targeted 400 nm span. The only solution would be to find an objective with a much larger aperture, but this is likely to cost a lot and I don’t think I will be able to do any better than f/1.4.

So you may wonder in which world is this an upgrade in regards to the previous setup that already had a ~100 nm span. But you should remember that we are now imaging each nanometer lines onto single pixels and so the setup has become much more sensitive to light. Also, stock lenses have really bad performance away from their optical centre and the quality of the spectrum is now much better, especially on the borders.

We can, however, still improve the setup by changing the lens L1 too. To do so, I have done some tests using several objectives/lens I had on hand. You can see them on Figure 2.

From left to right there is a stock lens, a microscope objective, a camera objective and the 6 mm imaging objective that I have used in the first part of this post. I will show how you can dramatically improve your spectrophotometer performance by replacing the stock lens by a SLR camera objective.

But first, let us recall the neon spectrum obtained in the older setup using a plano-convex 50 mm 1” stock lens for the collimation and a 35 mm 1” stock lens for the imaging. The spectrum is given on Figure 3.

Although it shows a relatively good resolution of the peaks from 580 nm to 640 nm, the rest of the spectrum is quite noisy. It had however a good dynamic range of 1:74 and a relatively good pixel-to-wavelength linearity with a r² fit of 0.9998. This has to be compared to the [»] commercial spectrophotometer of Science-Surplus who has lower linearity and lower dynamic range (only 1:32 in my previous review).

One would then expect that replacing the imaging lens with the 6 mm C-mount Navitar objective would already give some results but, although I spent a lot of time to align the setup, I got nothing but crappy results as can be seen on Figure 4.

There is a relatively high spreading of the spectrum but individual peaks can still be discriminated. Interestingly, the relative peak intensities changed completely and are now much more uniform. Finally, there is a much better definition of the peaks in the 640-680 nm region which appears now clearly. The pixel-to-wavelength linearity is still as good with a r² of 0.9986.

I was clearly not satisfied with these result and swapped the 50 mm plano-convex stock lens with a 4x microscope objective which corresponds to a focal length of about 45 mm. The results are given on Figure 5.

This is now starting to look quite good! The definition of the peaks is much better, even at the borders, and peaks that are distant of less than 2 nm are clearly distinguishable from each other (look at 640 nm). The intensity is also quite uniform and the linearity still unchanged (r² of 0.9984). I think that the added definition is due to the good chromatic performance of the objective which limits spreading of focal lengths and blurry results.

The quality however comes with a price: about $250US.

For that last reason, I gave a try to an old Nikkor 50 mm f/1.4 that my father gave me. The results are given on Figure 6.

The results are as good as the one obtained from the microscope objective for less than half the price (you can find these objectives on e-bay for less than $100US). The dynamic range even got better with a 1:85. Clearly, these lenses are good added value. Not only are camera objectives cheaper, they also have much larger apertures. For instance, the 4x Olympus microscope objective had a 0.1 NA which corresponds to a f/5 aperture while the Nikkor had a f/1.4! Larger aperture means more light and so a more sensitive setup. The major difference between Figure 5 and Figure 6 was the exposure time: 1 second for the former and 0.2 second for the latter. As a consequence, the Nikkor setup was 5 times more sensitive to light for half the price!

If you consider buying one, just take care to one little detail: get one that has an aperture ring, no matter if it is a Sigma, Nikon, Canon… objective. I first tried with a modern Nikkor AF-S 35 mm f/1.8 but the problem is that modern DSLR optics have no more aperture rings (‘G’ type objectives in the Nikon terminology) but a small spring-loaded pin controlled by the camera instead. In the case of the AF-S objective, I had to use rubber tape to hold the aperture pin to the “open” position. The rubber tape is not a good solution however because it goes off very easily… so you will have to use some tricks if you buy a modern objective. The advantage of the older ones is that you can finely tune the aperture manually.

In conclusion, I suggest upgrading your spectroscopy setup according to Figure 1 with a 50 mm f/1.4 SLR camera objective as collimating lens and a second 6 mm f/1.4 camera objective for the imaging lens used with a 5.2 µm CMOS sensor. They achieve high sensitivity and good chromatic behaviour which offers sharp peak definition over a 100 nm spectrum.