Interpolation apparatus for digital electronic position measuring instrument
BACKGROUND OF THE INVENTION 
     This invention relates to a process for interpolating position dependent periodic electrical signals generated by a digital position or angle measuring device. The invention is particularly suited for use with photoelectric measuring devices. 
     Incremental measuring systems of the prior art typically generate a series of electronic pulses whose number represents a measure of the change in the position or the angle of rotation being measured. These pulses are summed in an electronic up-down counter, and the sum is converted to a measurement value which is displayed numerically as a digital value. 
     The resolution capacity of such measuring systems is limited by the grid spacing of the precision measuring scale used. Attempts have been made in the past to improve the resolution of the digital measurement in such incremental measuring systems, especially through electronic measures. 
     In one well-known interpolation apparatus the primary analog signals from the scanning unit of the measuring device are phase-shifted to one another. These analog signals are applied to a resistance chain that includes a series of adjustable potentiometers. By tapping the potentiometers there can be generated a plurality of secondary signals that lie between the primary signals and thereby make possible an interpolation. The device disclosed in Swiss Pat. No. 407,569 is one example of such an interpolation apparatus. 
     In practice, interpolation devices with resistance networks for generating secondary signals are generally unsuitable for high resolution interpolation. The electronic circuitry expenditure required for interpolation rises enormously as the resolution of the interpolation rises. As a consequence, the high cost of high precision interpolating devices of the foregoing type is a significant drawback in many applications. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to an interpolation process that permits high resolution interpolation within a signal period with a relatively small expenditure for electronic circuitry. 
     In this process at least one electrical analog signal is digitized and the digital values are fed to a digital computer programmed to compute interpolation values. Further features of the process of the invention are set forth in the appended claims. 
     With the interpolation process of this invention no appreciable increase in electronic circuitry is required to increase the resolution of interpolation. Accordingly, high resolution interpolation which increases the resolution of the measurement by a factor of one thousand, for example, can be performed with a relatively small expenditure for electronic circuitry. Microprocessors which are widely available today as economically feasible components are preferably used in the invention. 
     The invention itself, together with further objects and attendant advantages, will be best understood by reference to the following description taken in connection with the appended drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic representation of a first measuring device embodying the interpolation process of this invention. 
     FIG. 2 is a schematic representation of a second measuring device embodying the invention. 
     FIG. 3 is a schematic representation of a third measuring device embodying the invention which is capable of interpolation while the measurement is changing. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Referring now to the drawings, FIG. 1 schematically represents a linear incremental measuring system including a scanning unit G, and grid scale M. The scanning unit G and the scale M may be mounted on the bed or on the slide piece of a tooling or measuring machine, for example. The scanning unit G and the scale M are slidable relative to one another in the direction indicated by the arrow. 
     The scanning unit G includes a grid scanning plate, a light source, and photosensors (not shown) which generate electric analog signals S 1 ,S 2  in response to the instantaneous position of the scanning plate with respect to the grid M. Signals S 1 ,S 2  vary in a sinusoidal manner and are phase shifted 90° to one another. The analog signals S 1 ,S 2  are fed to amplifiers V 1 ,V 2 , respectively, and the amplified signals are applied as inputs to the trigger circuits T 1 ,T 2 , which operate to convert the signals S 1 ,S 2  into square waves S 1  &#39;,S 2  &#39;. The square waves S 1  &#39;,S 2  &#39; are applied to a direction discriminator D, which is coupled to an electronic up-down counter Z. The counter Z counts pulses generated by the direction discriminator D using the appropriate sign to maintain an accurate total count. Measuring systems of the above-described type are generally known and, therefore, require no further explanation. 
     The present invention utilizes a digital computer R to interpolate position, i.e., to subdivide the periodic signals S 1 ,S 2  into a plurality of digital steps. Preferably a mincomputer or microprocessor is used for the computer R. 
     As shown in FIG. 1, analog to digital converters U 1 ,U 2  are used to digitize the analog signals S 1 ,S 2  and the digital values are supplied into the computer R for the calculation of interpolation values within a signal period. The counting result of the up-down counter Z and a binary control signal S 2  &#39; are also fed into the computer R. The computer controls the display unit A to display position values in numerical form which indicate the relative position of the scanning unit G with respect to the scale M. The computer R is programmed to combine the values of the full signal period provided by the counter Z and the computed interpolation values to generate an interpolated position value. 
     FIG. 2 shows another circuit for digitizing the analog signals S 1 ,S 2 . The circuit contains a digital to analog converter U 3  controlled by the computer R preferably a microprocessor. The output of the converter U 3  is applied to a first input of the difference trigger circuits T 3 ,T 4 , and the amplified analog signals S 1 ,S 2  are applied to a second input of the input trigger circuits T 3 ,T 4 , respectively. The signals generated by the triggers T 3 ,T 4  are transmitted to the computer R as input signals. Digitizing circuits such as the one just described are known to the prior art and are described, for example, on page 52 of the publication &#34;MCS-4 Microcomputer Set&#34; of the firm of Intel Corporation, Santa Clara; Users Manual, September 1974, Rev. 5 second printing. 
     One important advantage of the digitizing circuit shown in FIG. 2 is that the circuitry required to perform the desired interpolation is relatively simple and inexpensive to fabricate. 
     The circuit shown in FIG. 3 permits an interpolation to be made even during movement of the measuring system G.M. A pair of sample and hold circuits SP 1 ,SP 2  are provided on the input side of the analog to digital converter U 4 . Additional memory units (digital memories) SP 3 ,SP 4  are provided in the lines between the computer R and the trigger circuit T 2  and the computer R and the up-down counter Z, respectively. The sample and hold circuits and memories SP 1 ,SP 2 ,SP 3 ,SP 4  are controlled by the computer R to store the instantaneous values of their respective input signals on command. Of course, it should be understood that the aforementioned memories SP 1 ,SP 2 ,SP 3 ,SP 4  can also be controlled by an external command. 
     The embodiment of FIG. 3 also utilizes a single analog to digital converter U 4 . An electronic switch W is provided between the sample and hold circuits SP 1 ,SP 2  and the converter U 4 . This switch W is controlled by the computer R, to connect the circuits SP 1 ,SP 2  alternately to the converter U 4 . 
     In the preferred embodiments shown above the computer R can be programmed for high resolution interpolation. In such cases it is preferable to make certain corrections to the digital values input to the computer before the interpolation algorithm is applied. Preferably the digital values formed from the analog signals S 1 ,S 2  are corrected for symmetry by eliminating any DC offset, amplitude equality, and 90° phase shift. These corrections can be made with correction values stored in the computer R as a correction table. 
     The computer R can be programmed to calculate the interpolated position values P according to the following formula, for example: 
     
         P=N/2π arc tan (U.sub.sin /U.sub.cos) 
    
     
         if U.sub.sin ≦U.sub.cos 
    
     and, respectively, 
     
         P=(N/2π) arc cot (U.sub.cos /U.sub.sin) 
    
     if U sin  &gt;U cos   
     Where P is the interpolated position value; 
     N is the subdivision factor; and 
     U sin  and U cos  are momentary values of the voltages of the output signals S 1  and S 2 . 
     The corresponding programming of the computer R is familiar to the worker in the field and, therefore, requires no detailed explanation. 
     Of course, it should be understood that various changes and modifications to the preferred embodiments described herein will be apparent to those skilled in the art. For example, the invention is not restricted to the photoelectric measuring system described, but the interpolation system of this invention can also be used in association with inductive, magnetic, or capacitive measuring systems. Furthermore, the invention is not restricted to use with measuring systems employing sinusoidal analog signals but instead is also usable with other periodic analog signals, such as triangular signals, for example. Such changes and modifications can be made without departing from the spirit and scope of the present invention and without diminishing its attendant advantages.