Moiredemo is a simple computer demonstration designed to show how traveling wave patterns produce coarse, regular, and stationary intensity patterns.
Moiredemo doesn't precisely model the interference of coherent beams of light or draw accurate interference patterns. Instead, it uses a simpler pattern called a moiré pattern. Chapter 4 of the class notes refers to moiré patterns this way:
You may not have thought of it this way, but the moiré patterns ("more-ay" is an English mispronunciation of a French mis-transcription, "mwah-ray," of a Persian word (unpronounceable?) for a watermarked taffeta fabric) that are formed between two repetitive optical patterns is also a case of wave interference. You may have seen these between two pieces of window screening, chain link fences at a distance, muslin curtains, and so forth (printers worry about them in color halftone printing, too!). The mathematics of multiplying two repetitive or wave-like patterns is the same as the mathematics of adding and squaring them (that is, interference!)...
You may have noticed moiré patterns formed between two screens in front of a window, or between two pieces of chain-link fences. Since coarse, repetitive patterns are not uncommon in the world, moiré patterns are also not that uncommon. True interference patterns are less common (or perhaps less noticed) than moiré patterns in part because the frequency of the pattern is proportional to the the frequency of the repetitive physical or optical structure that caused it. Since the frequency of light's oscillation is so short compared to the pitch of a fence, interference and moiré effects manifest themselves to us in different ways.
Moiré patterns are not exactly like interference patterns. In particular, a moiré pattern is made from structures that vary from dark (0) to bright (or opaque to clear, etc.) while the electric field of a beam of light varies from a positive to a negative value. Moiré patterns can only add (or multiply), while an interference pattern can also subtract or "cancel" where the phase of light adds destructively. There's enough of a similarity between moiré and interference patterns, though, to use the former to learn about what's happening at the wavelength scale of light.
The
demo programThe moiredemo program simulates two crossing beams of light using a moving repetitive pattern of lines. The frequency (or pitch) of the two sets of lines is identical; so is their rate of motion. A moiré pattern forms where the lines intersect.
The program has two controls. The first varies the angle between the two beams. The second controls the relative phase between the two beams, as measured in cycles. In other words, the position of one of the sets of lines is shifted along its propagation direction by the fraction of a cycle given by the "Phase" slider.
Moiredemo shows a fringe pattern as it exists in space. If you could capture a moiré pattern using a photographic plate in the same way you can capture an interference pattern, the "plate" would be a line that intersects the path of the two "beams" in the demo. The pattern recorded on the plate would be the light and dark patterns at the surface of the plate.
Run the program, do the following operations, and think about answers to the following questions.