# Used in mathematics in cinematography

## cinematography

cinematography, General term for methods for the photographic recording of phase image sequences with sufficiently short-term successive, regular image changes and for reproducing the image sequences in such a way that the viewer regains the impression of the original movement. In the modern K., the sound events belonging to the visually perceptible processes are recorded and reproduced synchronously with the image.

1) Basics. The K. is based on the application of the stroboscopic effect (stroboscopy). The stroboscopic movement is one with sufficiently fast reproduction of a Phase sequence perceived apparent movement. This happens even though the individual images are only still images. The cause of this is Afterimage effect in the human eye. The most important variable is the physiologically based one Flicker fusion frequencywhich determines the image frequency (number of individual images per second) necessary for the merging of the individual phase images into one image with the apparently original, natural movement process. She's from that critical flicker frequency to differentiate, i.e. the interruption frequency at which lower values ​​are reached and the flickering of the projection image disappears for the viewer. Its value lies between 42 and 50 Hz. It increases with increasing image brightness. In order to exceed it, a Revolving fastener the interruption frequency is doubled (at 24 to 30 frames / s) or tripled (at 16 to 18 frames / s) compared to the frame rate.

The volume is made with the help of the Optical tone method recorded and played back. The voltages or currents supplied by microphones either influence the intensity of a slit image as analog signals or, processed in analog-digital converters, cause a light-dark change of a fine controlled light beam as digital signals. This enables the recording of a Optical soundtrack on the motion picture that was passed by. During playback, this track generates electrical current fluctuations by means of a photoelectric converter, which are fed to loudspeakers after amplification.

2) Film recording. Depending on the film production, different Film cameras used. The unexposed motion picture film is transported in them. A Film switchgear at the picture window ensures intermittent film transport. It effects the mechanical compensation of the image migration when recording the phase images. In addition, there is the optical compensation of the image wandering by means of rotating polygonal prisms, mirror polygons, swivel mirrors or lens rings, which map the phase images in the image window onto the motion picture film.

Film cameras come in many varieties. Modern embodiments are often equipped with automatic exposure and focusing systems. Cine film cameras often enable edge-track magnetic sound recording (e.g. Super 8 sound film) in addition to the image. Professional cameras for animated film recordings only use 35 mm film and have a frame-by-frame function for recording images. Time stretcher and high frequency cameras work with frame rates of 30 to 100,000 frames / s.

3) Film editing. This comprises the following work steps: The photographic layer of the motion picture film exposed in the film camera is developed into negatives or reversal positives using acetate cellulose or polyester as the layer substrate. Film positives that are ready to be reproduced are created with the former through additional copying, while the latter can be used immediately.