well done cfastie, thanks for taking the time to conduct some measurements. I've been pondering over the pattern and the angles for some time now. (see related postrs in the PLOTS-spectrometry list).
I'd like to add a few things to this, hopefully shedding some light from a High School physics teacher's perspective ! Sorry if some of it is dumbed down a bit, I'm writing for the whole audience.
Firstly, the "collimating slit" is purely to create a source that is in phase. The light (photons or waves, it matters not, there are ways to mathematically show the same effect either way) must be coherent. A jumble of incoherent waves hitting the DVD, since they have a random phase relationship, won't produce any pattern. There are two ways to achieve this, one is to look at a pinpoint light source from a great enough distance, the other is to create such a source by passing the light from a non-point source through a narrow aperture. Huygen's principle. There are formulas for working this stuff out and it is related to the distance a human eye can resolve car headlights as being a pair rather than a single source. The resolvable limit of two points close to each other each emitting light.
The link is a good discussion, from a high school level about different diffraction gratings.
as an aside, I confess to being a bit mystified by the pattern when you use the new DVD by itself to look at flouro or incandecent halogen lights to get the nice reflective rainbow. The sources are incoherent, but the reflection diffraction grating interference pattern is striking and not affected by the need for collimation nor by the size of the source. If anyone has an explanation, I'd be grateful !
anywho, in the transmission diffraction grating (as opposed to the reflective type) the wider the collimation slit that is used, the more light we get but the less fine the final interference pattern. I think this is because the wide aperture just shines a beam of light onto the grating, whereas a small aperture causes divergence of the beam onto a wider slice of the DVD grating and the more grooves that are illuminated, the better the resolution. The light that is incident on the DVD must still be coherent.
Looking at this and the possibility of a small divergence from a slit used to let light into the apparatus, I could imagine the further away the grating is placed from the aperture, the more grooves are illuminated and the better resolution that can be achieved, also altering the geometry slightly. This might be an explanation for the changing precision and need to re-angle the camera as the slit to grating distance is changed, but it is only a guess.
But the distance of the collimation slit to the grating shouldn't matter otherwise. The light from the single slit is simply being spread out (like waves through a narrow opening), the narrower the opening, the better the semicircular wavefronts on the far side (and the less the side effects which produce single slit interference). In our case, the opening is very wide in comparison to the wavelength of light, so a sizeable chunk of "straight" wavefront is allowed through and this is what the camera is focussing on after it has been diverged by the grating.
I suspect that the small changes in angle you observed are caused by very small changes in the angular alignment of the camera and DVD grating as you alter the distance. Your results show that doubling the distance involves an angle change of only 5 degrees or so. It must be very hard to keep everything lined up while you shift the opening and moving the opening side to side changes the geometry.
What is important are the two angles between the grating and the single slit and between the camera and the grating. Normally an interference pattern is observed by setting the grating at right angles to the source and viewing the pattern by projecting onto a screen (or eyeball). This is the form of the classic formula ml=d sin(theta) we use at school.
In the experimental setup we use, we place the camera sensor parallel with the grating and observe one side of the pattern, taking advantage of an asymmetry produced when an incident angle (angle between grating and slit) is introduced. This angle produces an asymmetric pattern, one one side we have:
sin(theta i) + sin(theta d1) = l/d
and on the other side we have
sin(theta i) - sin(theta d2) = l/d
theta i = incident angle of the light onto the DVD
theta d = angles of observed maxima from the grating.
l = wavelength of light
d = diffraction grating spacing
(note, I have deliberately changed the signs of theta d so that it is obvious one is an addition, the other is a difference, text books simply incorporate that sign into a convention for how the angle is measured)
I think we use the second side of the pattern. With a largish value for theta i, this produces spectral maxima that fall within the viewing area of the camera.
This asymmetry can be easily seen by shining a laser through the DVD grating and projecting the interference pattern onto a screen. If the DVD is at right angles to the laser beam, the two laser spots will be equidistant from the central maxima. As the DVD is angled, one spot increases its distance and the other gets closer to the central maxima.
In our setup, theta i is around 60 degrees, so we expect to see red on the screen at an angle of almost zero (say, in the centre of camera image) and blue at an angle of 20 degrees. The exact positions will be determined by the distance of the camera from the grating, increasing it will move blue off the screen (still at 20 degrees though) ! These are rough back of envelope calculations, so don't take them as gospel.
The blaze phenomena I think is related to reflection gratings, not to transmission gratings ? (probably a bad guess on my part !) . And then it is related to a particular design of grating.