ECE516 Lab 2 ("lab2"), 2023 "What does a camera measure?"

That fundamental question about what a camera measures is what led S. Mann to invent HDR (High Dynamic Range) imaging in the 1970s/80s, and develop it further at MIT in the early 1990s.

Most research on image processing fails to fundamentally address the natural philosophy (physics) of the quantity that a camera measures, e.g. at the pixel level. In some sense the research gets lost in a "forest of pixels" and can't see the "trees" (individual pixels) for the "forest" (array of pixels).

You do a good job of studying forestry if you only look at forests and never individual trees. If we were to begin deeply understanding forests, we might wish to begin first by really undrestanding what a tree is.

Likewise we'll never really understand what an image or picture is if we can't first understand what a pixel (picture element) is.

Mann's philosophy that led to the invention of HDR was to regard a pixel as a light meter, much like a photographic light meter. Under this philosophy, a camera is regarded as an array of light meters, each one measuring light coming from a different specific direction. With that philosophy in mind, differently exposed pictures of the same subject matter are just different measurments of the same reality. These different measurements of the same reality can be combined to achieve a better and better estimate of the true physical quantity. This quantity is neither radiance, irradiance, or the like (i.e. it does not have a flat spectral response), nor is it lumminance or illuminance or the like (i.e. it does not match the photometric response of the human eye). It is something new, and specific to each kind of sensor. It is called the "photoquantity" or the "photoquantigraphic unit", and is usually denoted by the letter q. Often we'll regard the camera as an array of light meters, perhaps sampled on a 2-dimensional plane, thus giving us a array of photoquantities q(x,y), over continuous variables x and y, which may be sampled over a discrete array of samples, which we might write as q[x,y] using square brackets to denote the digital domain even as the range might remain analog, or at least "undigital" (Jenny Hall's take on "undigital"). A typical camera reports on some function of q, e.g. f(q(x,y)) or f(q[x,y]).

In order to really fundamentally understand what a camera measures, we're going to build a really simple 1-pixel camera. Since the camera has only 1 pixel, we won't be distracted by spatially varying quantities and thus we won't be distrated by the domain (x,y) or [x,y]. This will force us to focus on the range, q, and this range is in fact the domain of f. Thus our emphasis here is on dynamic range!

There are two parts to Lab 2:

• 2a. Build a light-meter; that will be your 1-pixel camera: Quantimetric/Quantigraphic sensing....
  
• 2b. Use your lightmeter to make a 1-pixel camera and capture its metaveillance (metavision).

• 2a.i Beginner: photocell plus multimeter;
• 2a.ii Intermediate: photocell plus microcontroller;
• 2a.iii Advanced: photocell pair in Whatstone bridge plus microcontroller with differential analog input.

Marking:

• 1/10 Electrical build, e.g. reading out the quantigraphic quantity, q.
• 1/10 Collect quantigraphic data from your lightmeter: obtain ordered pairs (f,g).
• 1/10 Plot g as a function of f (comparagraph).
• 1/10 Plot f as a function of q (response function).
• 1/10 Determine the mathematical relationship between f and q, based on the data for your camera and compare with the same photocell as measured in class. In your case you can also get the dark resistance (measure the resistance in total darkness) and do constrained regression (forced through that data point).
• 1/10 Mechanical+optical build of the 1-pixel camera (nice box with pinhole or lens).
• 2/10 While observing numbers coming out of your camera (or a plot), move a point light source back-and-forth to determine your camera's field-of-view at various distances from the Aperture (pinhole or lens). A small Lamp (shown in red in the diagram) works best, e.g. perhaps the LED that was given out in class. Record the position of each of the points where the light falls to about half what it is inside the camera's field-of-view. These are the bondary points. For simplicity, confine the analysis to a plane (2D slice) passing through the optical axis (O.A.). The O.A. is a line drawn through the center of the Aperture, perpendicular to the image plane where the Photocell is located. It intersects the image plane at the Principal Point (P.P.). See the diagram below.
  
• 2/10 Using Octave and OpenBrush as a 3D plotter, plot a box (rectangle) that represents the camera, together with the camera's metaveillance flux as concentric arcs within the plane of your measurements, and capture by way of a screenshot of your OpenBrush screen. Draw all the arcs with the same center which should be the center of the Aperture. You can use "monoscopic" mode for this. The result might look something like this, but you don't need that many arcs, just keep it simple if you prefer:
  
• Optional (can get more than 10/10): Make some measurements in 3D (three dimensions), e.g. perhaps in two intersecting planes, or around circles or rectangles and Plot the metaveillance flux in 3D, together with a photograph of your camera in the extended metaverse (rather than just drawing a rectangular box to represent the camera). It might look something like this (below is the rectangular field of view of the infrared depth camera of a Delta automatic flushometer in the 3rd flr. men's room of Engineering Annex):
  
  or it might look something like this (just showing the outlines):
  

Post your results to this Instructable (One-pixel Camera...) on or before Wed. Feb. 15th at 3pm, and then bring to class Thu. Feb. 16th 9am for presentation..

Optional fun: you can compare with other data gathered in a previous year's lecture (link) and with the data gathered from the Blue Sky solar cell (link)

See also the Photocell Experiment. and the Instructable entitled Phenomenological Augmented Reality: