Measuring Reflectance with a Digital Camera

[brainpushups]

Background: This fall our initial plan will have high school students on campus 1 day per week and working remotely for the remainder of the week. I'm trying to plan for some at-home labs and projects. I came across http://albedodreams.info/how_to/how-to-calculate-albedo-yourself/ site which claims that albedo can be measured with a digital camera by using the histogram feature in ImageJ by comparing the mean intensity of the surface in question to white paper which, according to the site (and others I crossed referenced), has an average albedo of 0.65.

I tried out the method on the site using a gray card to see if I could calculate the albedo of printer paper. Gray cards supposedly have an 18% reflectance across the visible spectrum. I used my digital camera set to a given white balance (shade) and took several photos of the gray card and a piece of printer paper. Using the 18% value the range of white paper albedo values (7 measurements) ranged from about 0.50 to 0.56 using the average intensity. I also tried photographing the paper and gray card in the same lighting conditions (indoor, LED bulbs) but with different white balance settings and the values ranged from 0.46 to 0.51.

I can absolutely live with a fluctuation of 10% for this application, but I'm curious about the validity of this measurement method, especially since there seems to be a large systematic error. Further, there is definitely a large difference in the RGB histograms for the gray card depending on the white balance setting so I'm doubtful about the accuracy of using the histograms for measuring reflectance

What do you think? Is this method of determining albedo reliable? Could it be improved?

I'm thinking students could use this information for experiments about albedo's affect on surface temperature or maybe an engineering design project on solar ovens. Those ideas can be pursued without these albedo measurements, but the data would be categorical instead of quantitative.

PS
There is also an app one can purchase for $1 that claims it measures albedo using photos taken by a smartphone. At a cursory glance it seems to rely on the same method.

 

[Drakkith]

Hmmm. If the students are supposed to use their own phone cameras then this may be very difficult, as you can't really control the settings on most of those cameras very well. I suppose you could try the app out and see how well it works. It's only $1 after all.

 

[Ibix]

Looks like a fun experiment. I can offer a few thought about your variability issue, in no particular order.

You could also try the OpenCamera app, which is free. It let's you do things with a phone camera like lock the focus and exposure. That would prevent a phone trying to "improve" your picture, which might well mess with your results. Note that, with locked focus, you'd have to be a fixed distance from your surface with the camera - hopefully you were anyway.

You need to be careful that you don't have significant height at the high end of the histogram. That would indicate that the sensor is saturating and you are under-recording the brightness in some areas. I note that the example in the site you linked has exactly this problem.

Related to that, watch for specular reflections. If you are getting specular reflection from one surface and only diffuse reflection from the other that would mess up the histograms. If repeating the experiment in different places in the room changes the results, this is likely to be part of the problem.

You were doing your tests inside - how well did you control extraneous light sources? A good test would be to set up the camera, paper and card illuminated by a desk lamp (doesn't need to be uniform illumination for this test) and cover the whole thing with a cardboard box (might be easier to have the camera outside looking in through a hole in the box) to exclude all light except what you put in. Then see if that improves your replicability (students don't necessarily need to do this, but you might like to).

I'd aim to make sure that the piece of paper was the same size in every shot. A better way of doing it might be to have the white area cover one half of the shot, so you have the same optical setup working on your control and test regions.

White balance will absolutely affect this. The brightness histogram will be an average of the three colour channels' histograms, and the white balance tweaks the colour channels independently. I'm not sure that there's a "right" setting, but definitely keep it locked if that's an option.

 

[brainpushups]

You need to be careful that you don't have significant height at the high end of the histogram.

Thanks for the thoughts!

As per the saturation issue: on the 0-255 scale that is used how high do you think is too high? I took several photos of paper in direct sunlight and had values for average intensity around 245.

Related to that, watch for specular reflections

Indeed, I thought of that. Before I got the gray card I tried using a piece of glass to cover the paper and another surface (brown paper) to see if there was at least rough agreement with Fresnel's equations for normal incidence. There was a reduction in intensity, but not as great as I would have expected.

Then see if that improves your replicability

Due to the systematic difference from the 'textbook' value for white paper I will probably perform a more careful set of tests so they have that value to use, potentially instead of 0.65±0.05 (uncertainty based on the range of albedo in the online sources I found). I'm not sure if the sensor in my XT-3 will behave differently than a smartphone. They could compare their calculations to another 'textbook' surface (say, asphalt) and see which has greater agreement.

Thanks!

 

[sophiecentaur]

The main problem seems to be the unavoidable difference in time between when you do your moon and paper measuremtnts. It struck me that you need a way of 'transferring' between times (a home made standard). If you take a nice bright halogen lamp (similar colour temp to the Sun) and illuminate the sheet of paper, then compare the RGB figures with the Moon. Next day, do the same thing with the paper illuminated by the lamp and the Sun. The lamp illumination is common at both times so you can deduce a valid comparison between the Moon and the Paper, illuminated by the Sun.
I think my logic is OK. Please shoot it down if you can see a problem.

The hardest part will be explaining that procedure to the kids in a way that they will all understand what the heck it's all about.

 

[anorlunda]

Summary:: Can it be done with reasonable precision for the purposes of an at home lab during remote learning?

I'm thinking students could use this information for experiments about albedo's affect on surface temperature or maybe an engineering design project on solar ovens. Those ideas can be pursued without these albedo measurements, but the data would be categorical instead of quantitative.

I see the learning value of understanding albedo and methods of measuring it. I do not see additional learning value to 10% precision of the measurement. As long as the measurement shows that a dark surface has a lower albedo than a light one, what difference does the precision of the measurement make?

 

[hutchphd]

Some years (20 +) ago we looked at designing a low cost hand held colorimeter using a color CCD. I concluded it was not the best way to go (we needed pretty good precision ) but I think it should be sufficient to your needs ...I would guess 5% CV for diffuse reflectance of reasonably bright stuff is possible...maybe worse at dark end
A few thoughts( some of these duplicate the good advice above):

1. To measure diffuse reflectance try to avoid the specular direction scrupulously. Illuminate from an angle and detect from the same side of normal
2. I loved ImageJ software then, and I think it is still available and free. Allows you free manipulation of an image file
3. Obviously disable all the camera auto stuff so you know what you are doing, including white balance. I don't know the software available for this or what it does
4. For your experiment sunlight or filament bulb light at good brightness is preferred. Fluorescent and LED are pretty bumpy spectra.
5. Most CCD cameras are quite linear through the entire pixel digitizing range. Using a second additional gray standard low enough to "bracket" the desired range is even tighter for interpolation while you are experimenting.
6. Using the brightest white standard you can find for calibration will give better precision. For paper beware the "brightness" an "whiteness" difference.
7. Titanium Dioxide powder is cheap. Maybe the paint store could assist and their colorimeters are pretty good I think I got to know the guys at the art supply store near our lab pretty well and they were helpful when I was formulating test standards
8. You need to maintain the exact geometry for test standard and sample or Lambert's law of cosines will get you

This seems like a very good idea to me and please keep the results as public as possible. Write them up here!

 

[brainpushups]

I see the learning value of understanding albedo and methods of measuring it. I do not see additional learning value to 10% precision of the measurement. As long as the measurement shows that a dark surface has a lower albedo than a light one, what difference does the precision of the measurement make?

I agree that for the students that is the important concept. I was asking about the accuracy for my own benefit. But... if there are some simple things that can be done to improve the accuracy and reduce bias in measurements, why not do it?

I don't skip teaching students how to zero a balance before experiments involving Newton's laws. The important concept might be that increasing mass decreases acceleration, but I still want them in their lab work to try to measure precisely.

 

[brainpushups]

Maybe the paint store could assist and their colorimeters are pretty good I think I got to know the guys at the art supply store near our lab pretty well and they were helpful when I was formulating test standards

That's a cool idea. I had to go to the hardware store today anyway so I checked out the colorimeter. I used to work in a paint store as a teenager and used one for color matching. I couldn't remember what information was available in the menus, but at this particular store it is limited to the pigment formula. No information about the sample could be obtained.

 

[brainpushups]

I finally had a chance to think about this again after several weeks. I was much more careful in setting up the conditions for the camera but still wasn't able to get results that I trusted. So I bit the bullet and got the app so I could compare the results.

I tried three surfaces: cardboard, stone, and grass. The photos were taken in sunshine except the grass photos (and corresponding gray card photos) when the sun went behind a large cloud, but the lighting was very similar for every set. Edit: For clarification, I did not use white paper. Instead I was comparing results using the gray card

The results are reasonably close though I only did a single trial for each. The app reports to the hundredths place. I took the ratio of the mean intensities for the surface to the gray card (read from the ImageJ histograms) and multiplied by 0.18 (the reflectance of the gray card):

Surface	App Value	Camera Method Value
Cardboard	0.28	0.23
Stone	0.09	0.10
Grass (likely low due to shadows)	0.03	0.06

So it appears that students without a smartphone could get reasonable results by using a gray card. I don't think white paper will work very well. According to the app the white paper's albedo is 1.0, but that doesn't produce sensible results when taking ratios - they're systematically high.

Here's an interesting observation though: To double check the ratio method I downloaded the photos from the phone that the app used, imported them to ImageJ and tried the ratio method. The results were nowhere close to the app itself:

Cardboard: 0.19
Stone: 0.17
Grass: 0.13

So what's up with that? Maybe the software reads the photo data and somehow corrects for it? On the digital camera I held the aperture, shutter speed, iso, and white balance constant, but not on the phone.