Sources page biographical material

6.BH. MOIRÉ PATTERNS
I have not yet found any real history of this topic. One popular book says moirés were first made in 15C China. The OED has several entries for Moire and Moiré. It originally refers to a type of cloth and may be a French adaptation of the English word mohair -- Pepys refers to 'greene-waterd moyre' and this is the earliest citation. In the early 19C, the term began to be used for the 'watered' effect on cloth and metal. At some point, the term was transferred to the optical phenomena, but the OED does not have this meaning.
Journal of Science and Arts 5 (1818) 368. On the Moiré Metallique, or Fer blanc moiré. ??NYS -- cited in OED as their first citation for the noun use of the term.

John Badcock. Domestic Amusements, or Philosophical Recreations, ... Being a Sequel Volume to Philosophical Recreations, or Winter Amusements. T. Hughes, London, nd [Preface dated Feb 1823]. [BCB 16-17; OCB, pp. 180 & 196. Heyl 21. Toole Stott 78 80. Wallis 34 BAD. HPL [Badcock]. These give dates of 1823, 1825, 1828.] Pp. 139-141, no. 169: Moiré Metal, or Crystallised Tin & no. 170: Moiré Watering, by other Methods. "Quite new and splendid as this art is, .... M. Baget, a Frenchman, however, claims the honour of a discovery of this process, attributing the same to accident, ...." Cited in the OED as the first adjectival use of the term, though the previous entry seems to also have an adjectival usage.

Rational Recreations. 1824. Experiment 16, p. 15: Metallic watering, or, fer blanc moire. Says it is of Parisian invention and gives the method of applying sulphuric acid to tin.

Endless Amusement II. 1826? Pp. 24-25: Application of the moiré métallique to tin-foil. This deals with obtaining a moiré effect in tin-foil and is quite different than Badcock.

Young Man's Book. 1839. Pp. 312-314. Identical to Endless Amusement II.

Tom Tit, vol. 2. 1892. Le papier-canevas et les figures changeantes, pp. 137-138. Uses perforated card.

Hans Giger. Moirés. Comp. & Maths. with Appls. 12B:1/2 (1986) [= I. Hargittai, ed., Symmetry -- Unifying Human Understanding, as noted in 6.G.] 329 361. Giger says the technique of moiré fabrics derives from China and was first introduced into France in 1754 by the English manufacturer Badger (or Badjer). He also says Lord Rayleigh was the first to study the phenomenon, but gives no references.