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How many photons do I have?
THIS GUIDE IS FOR:
Persons who want to learn how many photons they have in their experiment
THIS GUIDE OFFERS:
An easy, step-by-step guide for measuring photons
It seems like a difficult question that would require sophisticated equipment and complex measurements to figure out. But it turns out you can get a pretty close estimate of how many photons are in a given pixel using some simple math and equipment you already have.
Cameras output image brightness information in grey values. In the literature, you sometimes see image intensity data expressed as “ADU’s” or “DN’s” (arbitrary digital units or digital numbers). The point here is that the grey values are, in fact, arbitrary. The good news is that it’s possible to back-calculate and know how many photons were detected. Here’s how to do it.
- Take an image of your sample under conditions that would be normal for your experiment.
- Determine the camera offset value. Digital cameras generally have an offset to prevent the clipping of very small signals that, due to noise, could end up below zero when digitized. The nominal offset value is typically indicated in the instruction manual, but you can also measure it. Block off all the light to your camera and take another image. If you are using your camera with microscopes setup, keep in mind that even if you pull the beam splitter to a position where ostensibly no light hits the camera, most microscopes have small light leaks that will change the image data. The best bet is to remove your camera from the microscope, re-install the dust plug that came with it, and take a dark reference image. Find the spatial average of this image by calculating the average intensity (in grey values) of all the pixels. The image should be pretty uniform so you can just estimate the average if you’d like. This average grey value is approximately the camera’s offset.
- Subtract the offset from each pixel in the sample image. Most image analysis software packages have very straightforward tools for doing this calculation as well as the calculations in the next two steps.
- Convert grey values to electrons by dividing each pixel in the image by the conversion gain of the camera. This spec is sometimes referred to as the “conversion coefficient” or “conversion factor”. All digital cameras have one, and Hamamatsu’s sCMOS cameras come with documentation giving this value for each individual camera. If you don’t have this number you’ll need to get it from the camera manufacturer.
- Now the moment of truth! Convert the electrons to photons by dividing the number of electrons in each pixel by the quantum efficiency (QE) of the sensor at the wavelength you are imaging. You can get this number from the camera’s spec sheet.
That’s it. Now you have the number of photons for each pixel. Of course there are many variables such as filters, optics, reflections, etc. that could move the numbers in one direction or another. But this method is accurate to within a few percentage points.
- Confirmation
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