The Poor Man’s Reflectivity Test

How good is the coating on your mirror? Labs answer that with a spectrophotometer. The Poor Man’s Reflectivity Test (PMRT) answers it with a digital camera: photograph something matte white standing on the mirror, then compare how bright the white object is directly and in its reflection. The ratio, worked out separately for red, green and blue, is the mirror’s reflectivity.

It is especially useful to people who spray silver their own mirrors, because silver tarnishes, and the question that matters is “how much have I lost since the day I coated it?” A cheap test you can repeat in five minutes is exactly the right tool for that.

Where it came from

The test was introduced on the Cloudy Nights ATM forum on May 11, 2019, by Tom (“totvos”, Mississauga, Ontario), whose circle of telescope makers was experimenting with home silvering and wanted a way to monitor tarnish against a baseline. Later that year (August 2019) Rob Brown published a much more careful treatment on the Spray Silvering Telescope Mirrors site, validating the camera against a spectroradiometer and laser measurements.

What you need

  • A camera that can save RAW files. Any DSLR or mirrorless body will do; Rob Brown used a Fujifilm X-E2. A phone can work too, with some extra care: see Using a phone below.
  • A diffuse white target. A block of PTFE (Teflon), lightly sanded to a matte finish, is the usual choice; white paper works in a pinch.
  • A bright light, such as an LED flashlight.
  • Software that can read linear pixel values from a RAW file: ImageJ with the DCRaw plugin, or GIMP (after converting the RAW to a TIFF without applying any processing).

Doing the test

Set up

  1. Lay the mirror flat, face up, and stand the white target upright near its center, square to the mirror surface.
  2. Place the camera so it looks down at roughly 45° and sees the target and its reflection side by side in one frame. Stand back as far as practical: the more distant the camera, the more nearly the direct and reflected views see the target from the same angle.
  3. Mount the light as close to the lens as possible. Light from the side or above shades the target’s surface texture differently in the two views, and that can produce readings that are wrong, even above 100%.

Take the picture

  • Use full manual exposure. Rob Brown used ISO 320, 1/15–1/125 s, f/5–6.
  • Save RAW (RAW+JPEG is fine; just throw the JPEGs away).
  • Expose so the white target lands at about 25–75% of full scale. Never let it clip. Watch the live histogram.

Measure

  1. Open the RAW file with white balance set to “None”, as 16-bit linear data, with every other adjustment turned off. JPEG compression, white balance and gamma curves all distort the ratio, so none of them may touch the data.
  2. Make sure the black level has been subtracted. Every sensor adds a fixed offset to every pixel (on a 10-bit phone sensor it is often about 64 out of 1023). DCRaw removes it automatically; if you use another converter, check. An offset left in pushes every ratio toward 100%.
  3. Keep the red, green and blue channels separate.
  4. Select a patch on the directly viewed target, and record the mean value of each channel.
  5. Select the corresponding patch on the reflection, and record the same.
  6. For each channel:
reflectivity = mean(reflected patch) / mean(direct patch)

That is the whole test. Tom’s first published example, a freshly silvered mirror with an experimental anti-tarnish overcoat, gave:

Channel Reflected / direct Reflectivity
Red 168 / 170 99%
Green 166 / 170 98%
Blue 163 / 171 95%

The falling blue figure is the yellow tint of that overcoat, which is visible by eye in the photograph.

Optional: which wavelengths are you measuring?

Each camera channel responds to a broad band of color. Rob Brown found the effective wavelength of each channel by photographing a spectrum (from a Project STAR spectrometer) and taking a cross-section of it in ImageJ. For his camera these came to about 630 nm (red), 535 nm (green) and 470 nm (blue). You need to do this only if you want to compare your numbers with published reflectance curves.

Using a phone

Nothing in the method needs a big camera. It needs linear, unprocessed pixel values and manual control of exposure, and many phones can deliver both. Neither of the sources below tested a phone, so treat this section as reasoning rather than reported results. Phones also bring some pitfalls a DSLR does not.

Get true sensor RAW, not “computational” RAW

  • iPhone: Apple ProRAW is not plain sensor data. It is merged from several frames and processed before it is saved. Use an app that saves Bayer RAW instead, such as Halide in its plain RAW mode, or the camera in Lightroom Mobile.
  • Android: apps that save Camera2 RAW_SENSOR DNGs, such as Open Camera, or the stock Pro mode on many phones, give you real Bayer data.
  • Avoid night mode, HDR, and anything else that stacks several frames.

Lock everything manually

Fix ISO, shutter speed, focus and white balance. Auto exposure does not change the ratio within a single frame, since both patches are in the same shot, but it ruins comparisons from month to month, which is the main point of the test.

Watch out for vignetting

This is the big phone-specific problem. Phone lenses darken a lot toward the edges of the frame, often by a stop or more in the corners. Phone DNGs usually store a lens-shading correction as metadata, and DCRaw and the ImageJ plugin ignore it. If the direct and reflected patches sit at different distances from the center of the frame, the darkening biases the ratio. To manage it:

  • Keep both patches small and close to the center of the frame.
  • Take a second shot with the phone rotated 180°, so the two patches swap places, and average the two ratios. This cancels most of the error.
  • Use a telephoto lens if the phone has one, and stand back. (Some phones’ “2×” setting is just a crop of the main sensor, but in a crop the darkest edges are trimmed off anyway.)

Check the phone before trusting it

  1. Linearity: shoot the target at two shutter speeds one stop apart. The patch values should double. If they don’t, something in the pipeline is not linear.
  2. Repeatability: take 5–10 frames and compare the ratios. If they agree to within about 0.5%, as Rob Brown’s camera did, you are in good shape.
  3. Known reference (optional): test a mirror whose reflectivity you already know, such as a fresh first-surface mirror, or one you have measured with a real camera.

Smaller differences

  • Phones save 10–12 bits per pixel rather than a DSLR’s 14. That is plenty.
  • The small sensor is noisier. Averaging over a larger patch takes care of that.
  • Each channel’s effective wavelength will differ from Rob Brown’s camera. That matters only if you compare against published reflectance curves.

With the same phone, app, distance and lighting every time, a phone should be fine for tracking a coating over time. For absolute numbers, trust it a bit less than a DSLR until it passes the checks above.

How good is it?

Better than you might expect:

  • Repeatability: Rob Brown measured a standard deviation of no more than 0.28%, so repeated measurements agree to better than ±0.56% at 95% confidence. That is better than his own spectroradiometer setup (±1.2%).
  • Silver: on a 9-month-old silvered mirror the camera read about 96% across the spectrum, within 1–2% of the spectroradiometer and within the ±1% uncertainty of the laser measurements.
  • Enhanced aluminum: on an Edmund Optics enhanced aluminum mirror the camera read about 2–3% low, uniformly across the spectrum. Multilayer coatings are sensitive to angle of incidence and polarization, and the test views the mirror at 45°, not at the near-normal incidence a primary sees in use.
  • Against the lab: Tom found his uncorrected RAW results came within about 2% of laboratory results.

The catch, and why it mostly doesn’t matter

A sharp objection was raised in the original thread: light doesn’t reach the target only directly from the lamp. Some bounces off the mirror first. So each view is a mix of two light paths. Write R for the mirror’s reflectivity, B for the target’s back-scatter (light bouncing straight back toward the source side), and F for its forward-scatter (light that arrives from the mirror below):

  • the direct view sees B + R·F
  • the reflected view sees one more mirror bounce of both: R·F + R²·B

The measured ratio is therefore

R · (F + R·B) / (B + R·F)

which equals exactly R when the target scatters equally in both directions (F = B). Working the numbers, a matte target whose forward and back scattering differ by even 10–20% makes the test over-estimate reflectivity by only 1–2% for mirrors in the 80–90% range.

If you want to tighten this up, suggestions from the thread include:

  • lift the target off the mirror on a spacer;
  • use a baffled light that cannot illuminate the mirror directly, in a dark room;
  • keep the target as close to perfectly matte (Lambertian) as you can, and the camera well away from the path of any specular glint.

Limitations to keep in mind

  • Angle. You measure at roughly 45–60° incidence. For bare silver or aluminum that matters little; for enhanced or dielectric coatings it can matter a few percent.
  • Three bands only. You get three broad color bands, not a spectrum, and nothing in the ultraviolet.
  • It shines at comparisons. Tom’s own emphasis was that this is a way to track a mirror over time, with the same camera, target and setup, rather than an absolute measurement. Systematic errors largely cancel out of the difference between this month and last month. Quoting decimal places is not justified.
  • Keep perspective. A few percent of reflectivity is close to invisible at the eyepiece: an online limiting-magnitude calculator cited in the thread puts the gain from 88% to 95% reflectivity at about 0.1 magnitude. The test tells you when a coating is genuinely failing, not whether to worry about 1%.

Even poorer men’s tests

  • By eye: hold a white card beside the mirror and compare its reflection with the card itself. Tarnish shows up as yellowing and dimming.
  • Sky and light meter: measure a patch of sky through color filters directly, then via the mirror.
  • Laser and detector: measure a laser beam directly, then after a bounce off the mirror. It is precise, but the alignment is fiddly at the amateur level.

Sources

This page was researched and drafted with the help of Claude, from the sources above.