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84 2 Image formation

1. Compute and plot the focus distance z o as a function of the distance traveled from the
focal length Δz i = f − z i for a lens of focal length f (say, 100mm). Does this explain
the hyperbolic progression of focus distances you see on a typical lens (Figure 2.20)?

2. Compute the depth of field (minimum and maximum focus distances) for a given focus
setting z o as a function of the circle of confusion diameter c (make it a fraction of
the sensor width), the focal length f, and the f-stop number N (which relates to the
aperture diameter d). Does this explain the usual depth of field markings on a lens that
bracket the in-focus marker, as in Figure 2.20a?

3. Now consider a zoom lens with a varying focal length f. Assume that as you zoom,
the lens stays in focus, i.e., the distance from the rear nodal point to the sensor plane
z i adjusts itself automatically for a fixed focus distance z o . How do the depth of field
indicators vary as a function of focal length? Can you reproduce a two-dimensional
plot that mimics the curved depth of field lines seen on the lens in Figure 2.20b?

Ex 2.5: F-numbers and shutter speeds List the common f-numbers and shutter speeds
that your camera provides. On older model SLRs, they are visible on the lens and shut-
ter speed dials. On newer cameras, you have to look at the electronic viewfinder (or LCD
screen/indicator) as you manually adjust exposures.

1. Do these form geometric progressions; if so, what are the ratios? How do these relate
to exposure values (EVs)?

2. If your camera has shutter speeds of 1 and 1 , do you think that these two speeds are
60 125
exactly a factor of two apart or a factor of 125/60=2.083 apart?
3. How accurate do you think these numbers are? Can you devise some way to measure
exactly how the aperture affects how much light reaches the sensor and what the exact
exposure times actually are?

Ex 2.6: Noise level calibration Estimate the amount of noise in your camera by taking re-
peated shots of a scene with the camera mounted on a tripod. (Purchasing a remote shutter
release is a good investment if you own a DSLR.) Alternatively, take a scene with constant
color regions (such as a color checker chart) and estimate the variance by fitting a smooth
function to each color region and then taking differences from the predicted function.

1. Plot your estimated variance as a function of level for each of your color channels
separately.

2. Change the ISO setting on your camera; if you cannot do that, reduce the overall light
in your scene (turn off lights, draw the curtains, wait until dusk). Does the amount of
noise vary a lot with ISO/gain?

3. Compare your camera to another one at a different price point or year of make. Is
there evidence to suggest that “you get what you pay for”? Does the quality of digital
cameras seem to be improving over time?