The Fizeau Wedge and the Optical Flat

Newton's rings happen between a curve and a flat. Put two nearly FLAT surfaces together instead, with a hair's tilt between them, and the fringes become straight lines — one for every half wavelength of gap. Hippolyte Fizeau formalised this in 1862, and it turned interference from a philosophical demonstration into a shop-floor instrument. What makes it useful is that a fringe is a CONTOUR LINE. The pattern is a height map of the gap, drawn in steps of about three hundred nanometres, and you read the surface directly: straight fringes mean flat, curved fringes mean the surface bows, and the amount they curve measured against their own spacing IS the departure from flat. That last point is the whole reason it survives. You are not measuring against a ruler that could be wrong — you are measuring the fringes against each other. The tilt you introduced cancels out, and what remains is the surface. Every gauge block, seal face, mirror blank and lens surface made anywhere is checked this way, and the apparatus is two pieces of glass and a monochromatic lamp. It is the cheapest thing in metrology that produces a NUMBER rather than an opinion.