A paper describes a photogrammetric method for measuring the changing shape of a gossamer (membrane) structure deployed in outer space. Such a structure is typified by a solar sail comprising a transparent polymeric membrane aluminized on its Sun-facing side and coated black on the opposite side. Unlike some prior photogrammetric methods, this method does not require an artificial light source or the attachment of retroreflectors to the gossamer structure. In a basic version of the method, the membrane contains a fluorescent dye, and the front and back coats are removed in matching patterns of dots. The dye in the dots absorbs some sunlight and fluoresces at a longer wavelength in all directions, thereby enabling acquisition of high-contrast images from almost any viewing angle. The fluorescent dots are observed by one or more electronic camera(s) on the Sun side, the shade side, or both sides. Filters that pass the fluorescent light and suppress most of the solar spectrum are placed in front of the camera(s) to increase the contrast of the dots against the background. The dot image (s) in the camera (s) are digitized, then processed by use of commercially available photogrammetric software.