the present invention as illustrated in the figures is a twochannel ( two - input ) digital encoder embodiment having a scanning system contained in a housing 12 . in this embodiment , the housing supports bearings for the shaft 15 of a constant - speed electric motor with a rotor 16 and stator 17 . the two input shafts , namely , an inner shaft 18 and an outer shaft 19 , have the same axis as the motor shaft 15 . these inner and outer shafts carry an inner bracket 20 and an outer bracket 21 , respectively . the motor carries a magnetized disk 22 fixed to its shaft 15 . the source of illumination for an optical indication of one disk position can be either a lamp or a light - emitting diode . fig1 shows a fixed lamp 23 mounted on the housing 12 . one narrow slit or hole 24 exists in the disk 22 so as to pass some light originating at the lamp 23 once per revolution of the shaft 15 . a photodetector 25 is mounted on a housing - mounted bracket 26 to receive any light not shaded by the disk . the photodetector can be a photocell or other illumination - sensing device . an inner magnetism - sensing head 35 and a similar outer head 36 are mounted on the inner bracket 20 and the outer bracket 21 , respectively . each of these heads confronts a point or small area on the disk 22 , either by touching it or being very close . in each case , the confronting points form a circle or an arc of a circle , the exact point on the circle being determined by its respective shaft position . on the disk surface , an arc in each of these circles is magnetically loaded ; i . e ., a track of magnetic anomalies exists so as to generate pulses in the heads 35 , 36 as the disk is rotated past them . the method of forming these anomalies is well known to those skilled in the computer tape and disk memory art . fig2 shows a view of disk 22 in which , in this embodiment , the disk rotation is viewed to have a counter - clockwise direction . the disk radius which goes through the center of the narrow hole 24 is called the optical radius ; the position of this radius corresponding to the instant when the hole is aligned to develop a pulse from the photodetector 25 is called the optical position . the pulse from the photodetector is fed into a monostable multivibrator which is also called a one shot 39 . the output from the one shot is a pulse having a duration of , say , the time of one half of a revolution of the disk . more accurately , the optical position is the position of the disk 22 at the beginning of the output pulse from each one shot 39 . see fig3 . the one shots and other circuits are connected to the mechanical parts shown in fig1 by means of a cable 40 . some of the wires in this cable come from the magnetic heads . these head wires 41 , 41 must be flexible because the heads are positioned by the input shafts 18 , 19 . mechanical limit stops may be used to limit the shaft position ranges to , say , one half of one revolution each although these stops are not shown . if type t flip flops and an extra head are added , the measured ranges of shaft angles can exceed 360 °. since this embodiment is a two - input encoder , the circuitry makes two measurements simultaneously and contains two channels . channel 1 measures the angle of the outer shaft 19 and channel 2 encodes the inner shaft angle ; these are angles a 1 and a 2 , respectively . in channel 1 , an and gate 45 combines the pulses from the first head 36 with the complement of the pulse from the one shot 39 . it performs the boolean and function . the output is the head pulse train inhibited by the one shot . this output is fed to a counter 46 which is reset once per revolution . in channel 2 , a second and gate 47 and a second counter 48 perform a second digital measurement . in both counters , parallel binary bits from yo to yn indicate the shaft angles once each revolution of the disk . in the sequence in which they occur , the events which form a measurement of the position of shaft 19 are as follows : 2 . the disk rotates counterclockwise until the first magnetic anomaly ( bit ) in the outer arc of disk 22 appears under head 36 . at this instant in time , the first counter 46 begins to count . 3 . during the time required for the disk to revolve through the angle shown as a 1 in fig2 counter 46 is counting . the relative position of disk 22 and head 36 is now as shown in fig2 . this is the so - called optical position . 4 . at this position , the photodetector 25 triggers the one shot 39 and the gate 45 is inhibited . this stops the counter . 5 . by the time the one shot 39 returns to its stable state , the last of the magnetized bits has passed by head 36 . therefore , the count corresponding to angle a 1 remains for the rest of one revolution of the disk . angle a 1 is the position of shaft 19 . during the same revolution , the second counter 48 measures the position of the inner shaft 18 in a similar manner using head 35 and gate 47 . if no second channel exists , this becomes a one - channel encoder like other shaft encoders . because of the small space occupied by each magnetic head , it is possible to have many channels of encoding in one housing using one disk . the above embodiment assumes a uniform distribution of magnetic anomalies around a 180 ° ( say ) arc of a circle on the disk for each channel . however , because a reading head can serve as a writing head and because of the adaptability of this type of recording , it is practical for non - linear bit spacing to serve useful purposes . for example , consider the requirements for a trigonometric resolver instead of for an ordinary shaft encoder . that is , consider the requirement for the counter to measure the sine of a rather than a itself . let s represent the bit spacing and r represent the radius of a track of bits ( arc of magnetic anomalies ). let c represent a total count or a constant defined by accuracy specification . if fractional counts are ignored , summation can be considered to be equal to integration and the track will generate a sine wave if this simply means that instead of being a constant , the bit spacing s must be a function of the angle , a . in other words , a track s 1 can be used to generate a sine function of a 1 and , using a different pattern , s 2 can be used to generate a cosine function of a 2 . if shaft 18 and shaft 19 are tied together , the result is a sine and a cosine function of a single shaft angle . in fig1 and 3 , the representation of the photodetector 25 is somewhat non - standard . this serves to indicate a sensing system rather than just a photocell . in particular , the cylindrical part of what is shown could be a part of an optical fiber for reshaping the beam of light .