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Photographically Measured
Reflectivity of Telescopes (PMRT)
Rob Brown, August 14, 2019
(editor's note: at the bottom of this page is a link to download a pdf version of this article)
Introduction
Measuring the reflectivity of silver and aluminum coatings normally requires special equipment. While trying to baseline the reflectivity of silver and aluminum before and after durability testing I was using an expensive spectroradiometer, which I can access at my job. But this is inconvenient, both for me and for anyone else wanting to know how their coatings are performing. The advantages of a spectroradiometer are primarily that it produces wavelength-by-wavelength reflectivity measurements, and you get a nice pretty plot:
Spectroradiometer plots of coatings, average of 10 readings each. Error bars are +/-1.5%, typical for this instrument.
However, amateur telescope makers and users don’t really need this much information. In fact, there is merit to evaluating the quality of a mirror simply by looking at it to see if it is dirty or stained. An evaluation technique is to observe the reflection of a white card held adjacent to the mirror to compare the color and brightness to the card directly in view. If such a comparison could be quantifiable then it would become a useful means to measurement of reflectivity. A digital camera with red, green, and blue sensitive pixels can be employed in such a manner as to make photographic measurements of reflectivity of telescopes (PMRT, or “poor man’s reflectivity test”). But making it a precise and accurate light meter requires some care. I believe I have achieved a level of success that is worth sharing. The next figure shows compelling results:
Measurement of reflectance of Silver with Camera, Compared to Reference 1, three lasers, and spectroradiometer.
Magnified view of silver reflectance
The camera based PMRT fits very well with the spectroradiometer and laser results, as well as published data for electroless silver1. The measured silver was old, about 9 months, but it was stored sealed and wrapped in anti-tarnish cloth so the tarnish is at a minimum. The electroless silver1 spectral reflectivity is copied in the next figure, which covers near UV and near IR.
Silver reflectance from reference 1.
The test was repeated for the aluminum coating.
Measurement of reflectance of Aluminum with Camera, Compared to Reference 2 (Edmund Optics), three lasers, and Spectroradiometer.
For aluminum, the camera test is reading low, and uniformly so across the spectrum. The aluminum coating is enhanced, and it is believed to be from Edmund Optics2. Enhanced coatings have thin film stacks which are sensitive to both angle of incidence and polarization, which might contribute to the larger differences in this case. Both the spectroradiometer and camera measurements are made at 45 degrees angle of incidence.
The digital camera can be used to obtain accurate reflectivity measurements with very low resolution spectral content. As such, it may be useful for those wanting to know when the mirror coating is degraded to the point of needing to be cleaned or recoated. The rest of this report describes the equipment and process.
Camera Details
The chosen camera is a Fujifilm X-E2 mirrorless with lens Super EBC XF 18-135mm. Images were taken at ISO 320, exposure times between 1/15 and 1/125 second, at F/5 to F/6. The goal is to expose the white target to a middle level in the camera’s dynamic range. The resulting image might look dark, but it’s OK as long as the white level is somewhere between 25% to 75% of full well capacity.
The camera resolution is 4896 x 3264 (16 megapixels). The camera operates in full manual mode and produces RAW images. (I think the most important part is that the camera produces RAW images, the rest is just full disclosure.) Any camera with RAW support should suffice. Cell phones might not support RAW, although there may be options and they have not been tested.
A Bower UV filter is present on the lens.
Setup for Measuring Reflectivity
The key to obtaining a good reflectance measurement is having a good setup. When using a spectroradiometer one is required to have a very stable light source and careful alignment. This is because the instrument measures one spot at a time. However, a camera can take 16 million spots at once, so we can simplify greatly.
Instead of a stable light source a diffuse white object is needed. I started this project using a small rectangle of sanded Teflon, since it appears to be whiter than paper. (However, white paper might work too.) It is important that the Teflon not have any shine on its surface, so I sanded it with 220. I later found that even the sanded Teflon had some specular reflection, so I painted it with Krylon flat white. Results were unchanged.
The setup is a mirror laying horizontally with the white reflector sitting on top of it, and the camera viewing the assembly at a 45-degree angle:
Photograph of Teflon on Aluminum Mirror (Blue protective tape was freshly peeled from the coating and still partially covers mirror at right.)
As seen above, the Teflon is stood up on the center of a mirror so that its reflection can easily be viewed adjacent to the direct view. It’s these two images that we can compare for reflectivity. Note that the camera angle is about 45 degrees to the mirror’s surface. Unfortunately, we cannot take the image perpendicular or we won’t see the Teflon in reflection. To ensure repeatability I used a drafting triangle to sight along so that my camera angle is at least close to 45o. See side view below:
Side view of setup showing 45o drafting triangle aligned to intersection of mirror and white reflector. For measurements, the camera is sighted along the triangle.
Finally, it was found to be important to use a strong front light as close to the camera lens as possible. An LED flashlight will suffice. Top lighting and side lighting can create subtle shadows that are hard to see visually and in the camera images, but when present may cause the readings to go over 100% reflectivity (which was how they were discovered.) A combination of lighting is OK as long as the front light dominates.
PMRT setup diagram, showing placement of light source and ray paths.
In the diagram, Lc is the luminance of the card and Rm is the reflection from the mirror. It is important to understand that the card luminance, Lc is the product of Lambertian diffuse reflection of illumination coming from the source directly and from reflection from the mirror below. The diffuse surface integrates both beams into one, and integrated product becomes the reference, Lc.
The luminance of the reflected image of the card is L’c , and it should be clear that L’c = Rm*Lc.
Thus, the measurement equation is easy to construct and reduces nicely:
Mirror Reflectivity = L’c/Lc = Rm*Lc/Lc = Rm
For completeness, here is the setup using the spectroradiometer:
Spectrometer setups
The stable light source is a tungsten halogen lamp housed in a baffled integrating sphere. This produces a very uniform spot of light. The source is monitored with an internally mounted detector and regulated through a feedback loop. The light source is stable to less than a percent.
The laser measurements look a lot like the spectroradiometer setups, but with the light source being one of three lasers (660nm, 532nm, 473nm) and the spectroradiometer being a silicon detector connected to a laser power meter. The lasers are stable to 1%, which contributes enough error to cover the differences between all measurements.
Image Processing
Images are taken in RAW+jpeg mode, and the jpegs are discarded. RAWs are imported using the DCRaw plug-in within ImageJ and are analyzed in ImageJ (National Institutes of Health, https://imagej.nih.gov/ij/). The process is described here. Again, any image processing tool should work, if it has the capabilities described in this process.
Open the raw image by selecting Plugins>Input-Output>DCRaw Reader as shown below.
Navigate to your desired raw image:
Select “None” under white balance. This may be critical, as others have reported that white balance can skew the results.
Select 16-bit linear. Make sure all other boxes are unchecked. (Reminder: This process is what works for the Fujifilm X-E2. It might vary for other cameras.)
Click “OK”. Your image should open within a few seconds.
Select a rectangle in the direct image of the Teflon.
Capture a histogram using Crtl+H, and select “No” when asked to include all three images. The TIFF images are three-layers, red, green, and blue. We want data in each layer, and No keeps them separate.
The histogram window opens. Select “Live” to get data in real time.
The red channel data opens. Note that the scale bar at the bottom of the plot is shades of red. Note also that there is a slider at the bottom of the image window. Running the slider selects image layers (r, g, and b.)
In the histogram window note the mean and StdDev values. In this case, mean = 9537 and StdDev = 242. As long as StdDev is around 10X lower than the mean then we’re good. If not, then either you have selected more than the Teflon area, possibly the whole image, or there is a very bad illumination non-uniformity on the Teflon, such as a glint from a bright light. Record the mean in a spreadsheet.
Next, slide the slider in the image window to the middle. This will bring up the green data in the histogram (although the image won’t appear to change.) You should see the histogram scale bar turn green. If it does not turn green, check to see that “Live” is selected. Record the mean for the green channel, in this case 8928.
Repeat for the blue channel. I get 5400.
Now, slide the yellow rectangle to the lower image, the reflection of the Teflon in the mirror. Repeat all three measurements.
The example produces means of 9294, 8549, and 4996. Record these as r, g, and b values in your spreadsheet. Example:
The reflectivity is the ratio of the values in Reflection to the values in Teflon, so divide one by the other in the adjacent column, and format as percentage:
A bar chart or graph can be produced with this data. However, the wavelengths have not been defined at this point. Wavelength calibration is optional for general use, but was essential for comparison to other techniques and is described next.
Bar chart with color-coded low-resolution spectrum
Wavelength Calibration
The spectral bands of each of the camera’s color channels are made apparent by taking a photo of a spectrograph image using the Project STAR Spectrometer3 .
ImageJ has a cross-section tool that produces a plot of pixel position vs. pixel value. Select a rectangle across the spectrum, aligning the selection rectangle with the wavelength scale and then use CRTL+K. A graph of pixel position vs. pixel value will pop up, and this can be done in each color channel.
The data was exported to Excel using the List button in each window. Pixel position (pixel number, x-axis) was easily converted to wavelength using a scaling factor of 1609pixels/250nm.
Spectral plots of each color channel in the Fujifilm X-E2 camera.
Removal of the solar absorption lines was then performed by smoothing the data with a 10nm boxcar average:
Smoothed spectral plots
The weighted average for each color channel was then computed for the purpose of comparing the reflectivity in each color band against the spectroradiometer. (For the red channel, the low hump in the blue wavelengths was discarded as it is suspected to be stray light.) The results are:
These wavelengths are a useful approximation, but only that. The spectral reflectivity was plotted at these three wavelengths for comparison to spectroradiometer results in the first section of this paper. A more accurate method might be to use narrow band astrophotography filters to get precise wavelengths, however such a method requires more exposures, more processing, more light, and more investment.
Wavelength calibration is not critical to your success if you only wish to monitor the health of your mirror.
Repeatability
The described process was used to measure fresh silver in preparation for life testing. A new sample was prepared, so the numbers are not the same as in the prior example. To get an accurate repeatability, the setup was taken down and rebuilt between photographs. The same spot on the mirror was measured three times.
Standard deviation for the reflectivity measurements is no more than 0.28%, so the repeatability is better than +/- 0.56% (two standard deviations, or 95% confidence). The repeatability is good and will support long-term monitoring of mirror coatings as they deteriorate.
The spectroradiometer has a repeatability of +/-1.2% as shown in the first figure. It is a consequence of having a much more complicated setup, requiring separate measurements of a light source and its reflection, and depending on the light source to be very stable. In addition, the instrument itself has had repair and calibration issues over its long life (10+ years). Four measurements were made with the spectroradiometer and the farthest outlier was thrown out. The setup was taken down and rebuilt between each spectroradiometer measurement, however the light source and spectroradiometer were not turned off and restarted due to extensive time burdens on warm-up.
Conclusions
Is a digital camera a good tool for characterizing the reflectance of a mirror? Apparently so! For the purpose of monitoring a coating as it ages, especially a silver coating, this tool has great value. But it is not intended to be a check on the absolute reflectivity of a new coating, and especially not for holding a supplier to specified values. Nevertheless, the agreement between a spectroradiometer, a laser, and a camera is pleasing and hopefully useful to a majority of telescope makers and owners.
References
1 D. Nahrstedt, T. Glesne, J. McNally, J. Kenemuth, and B. Magrath, “Electroless silver as an optical coating in an operational environment”, APPLIED OPTICS / Vol. 35, No. 19 / 1 July 1996
2 Spectral data for Edmund Optics, Enhanced Aluminum https://www.edmundoptics.com/document/download/420779
3 Project Star Spectrometer https://www.arborsci.com/
Insights, Extras, Tips
If your camera has a live histogram view, use it to make sure you are not overexposing. Overexposure will result in bad data.
I stood well away from the setup and zoomed in with the lens.
Calibration notes: I did not use flats or darks as one would normally do with astrophotography and other scientific imaging. However, I do not believe that such efforts are necessary in this case, for several reasons:
1. The camera is already well-calibrated for its lens. Raw images are uniform and not very noisy.
2. The area of interest is small and centered on the detector. Field variation will be nil.
3. The images are well-exposed. There is no need to stack frames. And there’s no need to make a pretty picture.
Have I made too many assumptions? Please put this to the test and report back!
It may be useful to some to shoot through narrow band filters. I did one, using the Orion Ultrablock, 2” format, held directly over my camera lens. The Ultrablock is a 20nm bandpass filter optimized for OIII and Hb wavelengths. This band occurs in the crossover region of the camera’s blue and green filters, but it is also at the peak of the dark-adapted human eye (scotopic vision).
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