Question 7 of 7: Optical Colour Sensing

Question 7: Optical Colour Sensing (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

a) LEDs emit light in a narrow spectral band centred on a wavelength set by their semiconductor bandgap, so a red, green, or blue LED is already close to a "pure" primary colour without needing an external filter to select it — unlike a broadband white source, which would need a filter (and the light lost to that filter) to isolate each colour. LEDs are also inexpensive, physically small, low power, switch on and off essentially instantly (allowing the three colours to be strobed sequentially without any moving parts), and have long operating lifetimes with intensity that is easily and repeatably controlled through drive current.

b) A phototransistor has internal current gain $\beta$: the base region absorbs light and generates a small photocurrent exactly as a photodiode would, but that photocurrent is then amplified by the transistor action before it leaves the device, giving an output current perhaps a hundred times larger than a bare photodiode would produce for the same incident light. For very dim light this larger raw signal is easier to detect above the noise of the following circuitry, even though the phototransistor trades this gain for a slower response time, more device-to-device variability, and a less linear response than a photodiode — acceptable compromises when the light level itself, not speed or linearity, is the limiting factor.

c) A photodiode's responsivity (output current per watt of incident optical power) is not constant with wavelength — it varies across the diode's own spectral response curve. Because each LED emits at a different peak wavelength, the same photodiode produces a different output current for the same amount of reflected optical power depending on which LED illuminated the sample. A single calibration constant (counts per unit reflected power) is therefore only valid for one specific illumination wavelength; sharing one photodiode across three different-coloured LEDs requires a separate calibration constant to be established for each LED in turn.

d) Reflectance readings are also affected by the source-object-detector geometry (distance and angle, since reflected intensity falls off with distance and with the angle of incidence/viewing), the surface finish of the object (specular/glossy versus diffuse/matte reflection scatters light very differently), ambient stray light reaching the detector from outside the LED source, drift in LED output intensity with temperature or age, and non-uniformity, curvature, or orientation of the sample surface itself.

e) Illuminate a set of reference targets of known, certified reflectance (typically a white/light reference, a black/dark reference, and one or more mid-grey or colour-tile standards) with each of the three LEDs in turn, and record the photodiode's output for every reference/LED combination. This builds a per-colour calibration relating raw photodiode counts to true reflectance for that wavelength; the white and dark references in particular set the high and low calibration anchor points (scaling and offset) for each channel, and re-measuring them periodically corrects for LED intensity drift or photodiode aging between full calibrations.