US2856128A - Cathode ray tube function generator with interpolation - Google Patents

Description

Oct. 14, 1958 M. c. FERRE 2,

v CATHODE RAY TUBE FUNCTION GENERATOR WITH INTERPOLATION Filed July 14, 1955 5 Sheets-Sheet 1 I (DUPLED COUPLED DIVISION CIRCUIT SWITCH FIG. I

mmvron MAURICE c. FERRE HIS ATTORNEY M. C. FERRE Oct. 14, 1958 CATHODE RAY TUBE FUNCTION GENERATOR WITH INTERPOLATION Filed July 14, 1955 5 Sheets-Sheet 2 INVEN TOR.

MAURICE C. FERRE FIG. 2

HIS ATTORNEY Oct. 14, 1958 M. c. FERRE 2, 5

CATHODE RAY TUBE FUNCTION GENERATOR WITH INTERPQLATION Filed July 14, 1955 5 Sheets-Sheet s INTEGQATOR INVENTOR. 4 MAURICE C. FERRE BY 2 I HIS ATTORNEY Oct. 14, 1958 M. c. FERRE 2,

CATHODE RAY TUBE FUNCTION GENERATOR WITH INTERPOLATION Filed July 14, 1955 5 Sheets-Sheet 4 DFFERTIATOR| I ISOLA Bl-STABLE v -rg l AMPLIFER ULTMBRA I20 I20 I I2! FIG. 5

INVENTOR.

MAURICE c. FERRE HIS ATTORNEY Oct. 14, 1958 M. c. FERRE 2,856,128

CATHODE RAY TUBE FUNCTION GENERATOR WITH INTERPOLATION File July 1955 5 Sheets-Sheet 5 I50 (f) .LLLLLLU.

lax MW 'ms ATTORQIEY CATHODE RAY TUBE FUNCTION GENERATOR WITH INTERPOLATION Maurice C. Ferre, Ridgefield, Conn., assignor, by mesue assignments, to Schlumberger Well Surveying Corporation, Houston, Tex., a corporation of Texas Application July 14, 1955, Serial No. 521,983

11 Claims. (Cl. 23561) This invention relates to computers, and, more particularly, pertains to new and improved computers of the curve-scanning type.

In a curve-scanning computer, a desired function of two independent variables is represented on a screen by a family of curves toward which a beam of light is projected. Either the beam or the screen is continuously displaced to scan the curves with light energy and, as a result, the light beam is modulated into pulsations by the curves. Two independently variable quantities control the pulse modulation, for example, by being employed to adjust the position of the beam relative to the screen, and photoelectric means are employed to derive a pulsetype electrical signal corresponding to the modulation of the beam. The pulses in the electrical signal are counted thereby to derive indications of the instantaneous value of the function.

Obviously, with a computer of the foregoing type only discrete values of the dependent variable may be obtained. Moreover, if it is desired to provide greater accuracy of computation, the number of curves on the screen must usually be increased.

It is an object of the present invention, therefore, to provide new and improved computers in which a family of curves is employed featuring greater accuracy in computation than heretofore possible without requiring an increase in the number of curves.

Another object of the present invention is to provide new and improved computers in which a given accuracy may be maintained while the number of curves employed may be materially reduced.

A further object of the present invention is to provide new and improved computers of the curve-scanning type incorporating means for interpolating between successive curves.

Yet another object of the present invention is to provide new and improved computers which feature indications of a dependent variable essentially over a continuous range of values, rather than discrete values.

A computer in accordance with the present invention comprises screen means carrying at least a pair of curves and means for projecting radiant energy in a beam toward the screen means and intercepting the screen means at a selected position which may be between the curves. Means are provided for displacing the beam and the screen means relative to one another in a first direction from the selected position toward one of the curves and in a second direction from the selected position toward the other of the curves. The computer further comprises means responsive to modulation of the beam of radiant energy by each of the curves for deriving electrical signal undulations representing the distance between the selected position and one of the curves and the distance between the selected position and the other of the curves, and means responsive to these electrical signal undulations for deriving indications of the location of the selected position relative to at least one of the curves.

According to a particular embodiment of the inven- United States Patent 2,856,128 Patented Oct. 14, 1958 tion, the relative displacement between the beam and the screen means is essentially continuous in each of the two directions and the electrical signal undulations are in the form of pulses individually having a duration representing the respective distances from the selected position to each of the curves.

In accordance with another embodiment of the invention relative displacement between the beam and the screen means is reversed each time the beam is intercepted by one of the curves and the electrical signal undulations may take the form of respective positive and negative excursions of a wave individually having a duration representing one of the distances.

The novel features of the present invention are set forth with particularity in the appended claims. The present invention, both as to its organization and manner of operation, together with further objects and advantages thereof, may best be understood by reference to the following description taken in connection with the accompanying drawings in which:

Fig. 1 is a schematic diagram, partly in block form, of a computer constructed in accordance with one embodiment of the present invention;

Fig. 2 represents various wave forms which may be found in the computer illustrated in Fig. 1 and which are useful in explaining its operation;

Fig. 3 is a schematic diagram of a modification which may be made to the computer shown in Fig. 1 and featuring another embodiment of the invention;

Fig. 4 represents various wave forms useful in explaining the operation of the modification represented in Fig. 3;

Fig. 5 is a schematic diagram, partly in block form, of another computer constructed in accordance with the present invention; and

Fig. 6 represents various wave forms useful in explaining the operation of the computer shown in Fig. 5.

In Fig. 1 of the drawings, there is shown a cathode ray tube 10 provided with the usual electrode system 11 adapted to form and project a beam of electrons toward a fluorescent screen 12. The electron beam is under the control of a deflection system which includes a pair of horizontal deflection plates 13 and a pair of vertical deflection plates 14. Of course, deflection coils may be suitably employed in place of the deflection plates.

The electron beam from electrode system 11 is focused in a small spot on fluorescent screen 12 thereby producing a corresponding beam of radiant energy, preferably in the spectrum of visible light. The electron beam, and hence the light beam, is under the control of a first voltage that is applied to a pair of terminals 15 coupled to horizontal deflection plates 13 via a directly-coupled amplifier 16. It is also under the control of a voltage which may be applied to a pair of terminals 17 connected to the input circuit of a directly-coupled amplifier 18 whose output circuit is connected to vertical deflection plates 14. In addition, a triangular wave or sweep generator 19 is coupled via an intermediate stage of amplifier 18 to vertical deflection plates 14. Accordingly, a voltage of triangular form is applied to these plates and a vertically directed sweep trace of light energy is developed on fluorescent screen 12.

A transparent screen 20 inscribed with a family of opaque curves 21 is positioned adjacent fluorescent screen 12 so that the beam of light energy in the sweep trace on the fluorescent screen is projected toward screen 20. The curves 21 may, for example, represent successive values of a dependent variable, z, plotted in terms of two-coordinate values of two independent variables to define the function z=;f(x, y).

Since the spot of light on fluorescent screen 12 is periodically displaced in accordance with the sweep wave from generator 19, it is evident that the light beam and screen 20 are relatively and recurrently displaced in an essentially fixed angular direction; thus the screen is recurrently scanned with light energy in a direction that is always vertical. The voltages applied to terminals and 17 position the sweep trace in translation relative to screen 20 in response to the independent variables x and v thereby to determine the number of curves intercepted by the sweep trace during each recurrent scanning interval.

Light energy in the beam emitted from screen 12 is modulated in pulses by curves 21, and modulated light is concentrated by a condensing lens 22 on a photoelectric cell 23. Cell 23 generates a number of electrical impulses corresponding to the number of incident light impulses and its output is equalized in a pulse equalizer 24 which supplies corresponding electrical pulses of fixed amplitude and duration to an integrator 25. The integrator is coupled to a summation circuit 26, the function of which will be described hereinafter, in turn, coupled to an indicator or output device 27.

The portion of the apparatus thus far described, exclusive of summation circuit 26, is a complete computer of the type disclosed in the copending application of H. G. Doll, filed June 2, 1953, bearing the Serial Number 359,197 and assigned to the same assignee as the present invention. As there described in detail, since one end of the sweep trace is positioned in the x and y directions according to the values of the voltages applied to terminals 15 and 17, the number of curves 21 intercepted by the sweep trace, and modulating the beam, is dependent upon the variables x and y. A corresponding number of electrical impulses are supplied to integrator 25 which derives a voltage proportional to the number of impulses and this voltage is supplied to indicator 27 and indications are obtained of the value of the dependent variable.

For example, as shown on screen 20 in Fig. l, the upper end P of sweep trace T may be at a selected position produced by the voltages at terminals 15 and 17 such that it is between the second and third curves. During each complete cycle of the triangular sweep, the curves below point P are intercepted twice thereby to derive four pulses. Indicator 27, of course, is appropriately calibrated so that in response to the voltage developed by integrator 25 representing four pulses an indication of two units is obtained. It is obvious that at any position of the upper end P of trace T between the second and third curves, the same indication of the dependent variable is obtained. In other words, only discrete values of the dependent variable are possible.

In order to interpolate between successive values of the dependent variable, the automatic computer shown in Fig. 1 further comprises another cathode ray tube 30 provided with an electrode system 31 adapted to form and project a beam of electrons toward a fluorescent screen 32. The electron beam is under the control of a deflection system including horizontal deflection plates 33 and vertical deflection plates 34 which are coupled to terminals 15 and 17 via directly-coupled amplifiers 35, 36, respectively. Thus, the resulting light beam from fluorescent screen 32 may be positioned in the same manner as the beam from tube 12 to impinge at a point P on a screen 37 carrying a family of curves 38 which is identical to the family on screen 20.

A triangular wave generator 39 is connected via a coupling condenser 40 to an intermediate stage of directlycoupled amplifier 36 thereby to apply a vertical sweep voltage to vertical deflection plates 34. By reason of the presence of the coupling condenser, the resulting sweep of the light on screen 37 includes a portion T which extends from point P in an upward direction and a portion T which extends in a downward direction from point P. The light energy modulated by curves 38 is concentrated by a lens 41 on a photoelectric cell 42 which derives a corresponding electrical signal that is supplied to a pulse equalizer 42.

Triangular wave generator 39 is also coupled to an amplifier and an amplitude limiter stage 43 coupled via a differentiator 44 to one input circuit of a bistable multivibrator 45 and to one input circuit of another bistable multivibrator 46. Stage 43 is also coupled to the control circuit of an electronic switch 47 having its input circuit connected to equalizer 42' and its output circuit connected to the remaining input circuit of bistable multivibrator 45. In addition, stage 43 is coupled through a phase inverter 48 to the control circuit of another electronic switch 49 whose input circuit is coupled to equalizer 42. The output circuit of multivibrator 45 is coupled to an integrator 50 and the output circuit of multivibrator 46 is coupled to an integrator 51. These integrators are coupled to a summation circuit 52, in turn, coupled to a division circuit 53. The output of integrator 51 is also supplied to division circuit 53 whose output is applied to summation circuit 26 where it is combined with the output of integrator 25 for application to indicator 27.

In describing the operation of the portion of the circuit just described, occasional reference will be made to Fig. 2 which represents various wave forms in the circuit plotted to a common time scale. As shown in Fig. 2a, the output wave of generator 39 is of triangular form and by virtue of the presence of coupling condenser 40 a reference 55 is established so that the sweep on screen 37 extends above and below point P.

Stage 43 converts the triangular wave of Fig. 2a to the square wave of Fig. 2b having the same period and including positive portions and negative portions 61. The leading edge of positive portion 60 produces a positive pulse 62 in differentiator 44 which transfers bistable 45 from a first conductive condition to a second, at the same time the positive portion 60 of the square wave opens electronic switch 47. As the sweep moves upwardly along the path T the pulses 63 of Fig. 2d are derived due to the interception of the light beam by curves 38. These pulses are applied via electronic switch 47 to bistable multivibrator 45. The first of pulses 63 to arrive namely pulse 63, transfers the multivibrator to its first operative condition thereby to determine the duration of a pulse designated by the numeral 64 in Fig. 2). Of course, once multivibrator 45 is conditioned by one of pulses 63, successive pulses have no effect upon its operation.

During the portion of an operating interval between positive and negative portions 60 and 61 of the square Wave in Fig. 2b, a negative pulse 65, shown in Fig. 2c, is derived by differentiator 44 and supplied to multivibrator 46 thereby transferring it from a first condition of operation to a second. At this time, the sweep on screen 37 travels in the downward direction, T and pulses 66 are generated as the curves 38 are intercepted by the sweep. The first of these pulses, 66', restores the multivibrator 46 to its first condition thereby to determine the duration of a pulse 67 illustrated in Fig. 2g.

Thereafter, the change in voltage between portions 61 and 60 of the wave shown in Fig. 2b produces a positive pulse 62 (Fig. 2c) in difierentiator 44 and another cycle of operation is initiated. Thus, trains of pulses 64 and pulses 67 are derived. It is evident that the durations of pulses 64 and 67 of Figs. 2 and 2g are dependent upon the position of the selected point P, relative to the two curves 38 immediately above and below this point.

The pulses 64 produce a unidirectional potential in integrator 50 having a magnitude dependent upon their duration and similarly the pulses 67 produce a potential of a magnitude representing their duration in integrator 51. These two potentials are arithmetically added in summation circuit 52 and the ratio of the voltage in integrator 51 to the voltage in circuit 52 is obtained by circuit 53. In other words, a voltage representing the interpolated position of point P above the lowermost adiacent curve is derived by circuit 53 and combined in summation circuit 26 with the voltage representing the number of curves intercepted by sweep trace T on screen 20. Accordingly, the corrected or interpolated value of the dependent variable is supplied to indicator 27.

It is thus apparent that a computer constructed in accordance with the present invention is adapted to produce indications representative of values of a dependent variable throughout an essentially continuous range. Obviously, if additional accuracy is not needed, a given accuracy may be maintained although fewer curves are required.

In the modification shown in Fig. 3, the manner in which this circuit may be associated with the arrangement of Fig. 1 may be evident by observing that similar elements are identified by the same reference numerals.

The output of pulse equalizer 42 is supplied to both input circuits of a multivibrator 70 via coupling condensers 71 and 72 connected to the control grids of electron discharge devices 73 and 74. Individual anode resistors connect the anodes 'of devices 73 and 74 to the positive terminal of a source 75 of 8+ supply potential whose negative terminal is connected to the cathodes via a common cathode resistor 76. Grid resistors connect control grids of devices 73 and 74 to the negative terminal of source 75 and the usual cross-coupling grid-plate resistors 77 and 78 are provided. The negative terminal of source 75 is connected to the negative terminal of another source 79 whose positive terminal is grounded at point 80. The magnitude of the voltage supplied by source 79 is selected in a known manner so that potential variations which occur at the anodes of devices 73 and 74 occur above and below the reference level established at ground 80. The anode of device 73 is coupled to an integrator 81 including a series resistor 82 and a shunt condenser 83, and condenser 83 is coupled to an intermediate stage of directly-coupled amplifier 36.

A discharge circuit 84' is connected across condenser 83 and comprises gaseous discharge devices 85 and 86 having their anode-cathode current paths connected in back-to-back relation. Device 85 is provided with a bias battery 87 having a polarity and magnitude sufiicient to maintain this device in a unionized condition, and another bias battery 88 is similarly provided for gas tube 86. The output of pulse equalizer 42' is applied to the control grids of gas tubes 85 and 86 via respective coupling condensers 89 and 90.

The anode circuit of electron tube 74 of multivibrator 70 is coupled to an integrator 91. The integrator, in turn, is coupled to summation circuit 26 (Fig. 1).

In describing the operation of the circuit modification represented in Fig. 3, let it be initially assumed that condenser 83 of integrator 81 is discharged and that at some instant of time tube 74 of multivibrator 70 becomes conductive whereby the voltage at the anode of electron tube 73 is carried quickly from the level of gronud 80 to a given positive value. Thus, condenser 83 begins to charge, with its upper side positive relative to reference 80, and the voltage across it builds up in the manner represented by line 92 shown in Fig. 4a. This carries the electron beam of cathode ray tube 30 upward so that the light beam moves upwardly from reference point P on screen 37. At the instant the light beam intercepts the curve above point P a pulse of light energy is produced and converted to an electrical pulse by photocell 42. The corresponding positive pulse, represented by numeral 93 in Fig. 4b, applied by equalizer 42 to multi vibrator 70 reverses the condition of conductivity between tubes 73 and 74. At the same time, pulse 93 is applied via coupling condensers 89, 90 to gas tubes 85 and 86. Tube 85 alone immediately becomes conductive and the voltage across condenser 83 is reduced to zero. This change in voltage is illustrated by portion 94 of the curve in Fig. 4a and the sweep returns to reference point P'. Thus, the voltage at the anode of electron tube 73 of multivibrator 70 exhibits a positive undulation represented by numeral 95 in Fig. 2c.

With the condition of conductivity reversed between tubes 73 and 74, the anode of tube 73 is negative relative to the ground and condenser 83 begins to charge in a negative direction as indicated by curve portion 96 in Fig. 4a. This draws the light beam downwardly from reference point P and when the curve below the reference point is intercepted, a pulse 97 shown in Fig. 4b is derived which reverses the condition of conductivity between tubes 73 and 74 cf multivibrator 70. At the same time, pulse 97 causes gas tube 86 to ionize and condenser is quickly discharged bringing the sweep back to the position P' as the voltage drops along the curve portion 98 in Fig. 4a. The voltage at the anode of tube 73 thus exhibits a negative undulation 99.

Thereafter, the cycle of operation just described is repeated and the square wave of Fig. 4c is derived. It is evident that the ratio of one of the undulations or 99 to the period of the wave illustrated in Fig. 40 represents the relative position of point P' with respect to one of the two adjacent curves 38.

The corresponding inverse square wave exhibited at the anode of tube 74 (Fig. 4d) is supplied to integrator 91 which derives a voltage represented by broken line 100. This voltage has a magnitude dependent upon the duration of the negative undulations of the square wave of Fig. 4c. In other words, this voltage represents the position of reference point P' relative to the lower one of the adjacent curves and it is added to the voltage from integrator 25 (Fig. 1) in summation circuit 26. Consequently, interpolated values of the dependent variable are obtained.

In each of the systems of Figs. 1 and 3, cathode ray tube 10 is incorporated in what might be considered the dominant portion of the system, while cathode ray tube 30 is in the vernier portion. In other words, the optical system is duplicated for the dominant and vernier portions.

If desired, a single optical system may be employed incorporating time-sharing for the dominant and vernier sweeps. For example, if a complete cycle of 5 units of time is assumed, the dominant sweep can be performed during 4 units of time, while five to ten vernier sweeps are made during the remaining unit of each cycle. Obviously, time-sharing may be employed in either of the embodiments of the invention thus far discussed.

In Fig. 5 there is illustrated another form of computer embodying the invention and employing time-sharing. It comprises a time-base generator which may generate a sine wave at a frequency of, for example, 50 cycles per second. Generator 110 is coupled to a square wave generator 111 which provides a square wave of the same frequency for application to the control circuits of gated amplifiers 112 and 113. Generator 111 is also coupled to a phase inverter 114 whose output is supplied to the control circuits of gated amplifiers 115 and 116. Thus amplifiers 112 and 113 are operatively conditioned during the positive portions of the square wave developed by generator 111 while amplifiers 115 and 116 are operatively conditioned during the negative portions.

Time-base generator 110 is also coupled to a frequency multiplier 117, in turn, coupled to another square wave generator 118 which provides a square wave having a period one-half that developed by generator 111. Generator 118 is coupled to a triangular wave generator 119 whose output is supplied to the input circuit of gated amplifier 112. The output circuit of amplifier 112 is coupled to an intermediate stage of directly-coupled amplifier 18 thereby to supply a triangular sweep wave to vertical deflection plates 19 of cathode ray tube 10.

Square wave generator 111 is coupled to a diiferentiator and clipper stage 120 which supplies positive pulses via an isolating amplifier 120 to both input circuits of a bistable multivibrator 121. The pulse output of photocell 42 is also applied to the input circuits of multivibrator 121 via pulse equalizer 42' and gated amplifier 116.

The output of bistable multivibrator 121 is coupled to an integrator comprised of a directly-coupled amplifier 122 having a charging condenser 123 connected between its input and output circuits and provided with a load resistor 124. A pair of resistors 125 and 126 are connected in series across condenser 123 and the junction between resistors 125 and 126 and one output terminal of amplifier 122 are coupled to a direct-current clamp 127 which may, for example, be a diode circuit of known construction, supplied with pulses from amplifier 120'.

The integrator just described provides a sawtooth wave, as will be more apparent from the discussion to follow, which is supplied to directly coupled amplifier 18 via gated amplifier 115 and to a clipper 128 whose output circuit 18 coupled to a low-pass filter 129. Low-pass filter 129 is coupled to a voltage adder 130. Also coupled to adder 130 is a pulse counter or integrator 131 which is supplied with the output of photocell 42 via pulse equalizer 42' and gated amplifier 113. The voltages derived and stored by low-pass filter 129 and pulse counter 131 are additively combined in adder stage 130 and supplied to an indicator 132, which may be a voltmeter.

In describing the operation of the circuit illustrated in Fig. 5, occasional reference will be made to the wave forms of Figs. 6a through 611 which represent the signal conditions at various points in the circuit all plotted to a common time scale. While a time base of 50 cycles per second has been specified, obviously any other time base providing a desired speed of operation of the computer may be utilized. This time base of 50 cycles per second is represented by'sine curve 140 in Fig. 6a having a repetitive period of 20 milliseconds. This period constitutes a complete operating cycle for the computer shown in Fig. 5.

The time base is supplied to square wave generator 111 which derives the corresponding square wave of Fig. 6b having positive undulations 141 and negative undulations 142. By virtue of the circuit arrangement, positive undulations 141 transfer gated amplifiers 112 and 113 from inoperative to operative condition, while negative undulations 142 transfer gated amplifiers 115 and 116 from inoperative to operative condition to provide a time-sharing function that will be more apparent in the discussion to follow.

From the signal produced by generator 110, frequency multiplier 117 produces a sine wave 143, represented in Fig. 6c, having a period one-half that of the sine wave 140. In response to wave 143, square wave generator 118 derives the square wave of Fig. 6d having positive undulations 144 and negative undulations 145 and in response to square wave 144, 145 triangular wave generator 119 produces the wave of Fig. 6e having positive-going portions 146 and negative-going portions 147. Those of the wave portions 146 and 147 which occur during timeportion 141 of the square wave shown in Fig. 6b, i. e. when gated amplifier 112 is operatively conditioned, are applied to vertical deflection plates 19 of cathode ray tube and a vertical sweep is developed in the same manner as described in connection with the sweep derived for cathode ray tube 10 of the arrangement illustrated in Fig. l. The position of the sweep, of course, is dependent upon the voltages applied to terminals and 17 thereby to determine the number of pulses in the modulated light beam which is intercepted by photocell 42. Accordingly, electrical pulses are supplied via gated amplifier 113 to pulse counter 131 which develops and stores a voltage representing the number of pulses.

During the following interval in which undulation 142 of the wave in Fig. 6b occurs, the amplifiers 112 and 113 are disabled and the function of the dominant sweep is discontinued, and the amplifiers 115 and 116 are operatively conditioned.

When the voltage developed by generator 111 changes from the value 141 to the value 142, differentiator and clipper stage produces a pulse 148 (Fig. 6f) which operates direct current clamp 127 thereby bringing the voltage across condenser 123 to a value of zero. At the same time, pulse 148 transfers multivibrator 121 from a first to a second operative condition so that a voltage begins to build up across condenser 123 as illustrated by portion 149 of the curve represented in Fig. 6g. This causes the beam of light to move from the position P in a downward direction and when the next successive one of curves 21 is intercepted, a pulse is developed by photoelectric cell 42 and is supplied over gated amplifier 116 to multivibrator 121. This pulse, denoted by numeral 151 in Fig. 6f, returns the multivabrator to its first operative condition and the polarity of the current supplied to condenser 123 is reversed. Thus, the voltage across the condenser changes, as shown by portion 152 of the curve in Fig. 6g and the light beam moves upwardly along screen 20. Upon the interception of the curve above the reference point, P", a pulse is derived by photocell 42 which is supplied via amplifier 116 to multivibrator 121 reversing its condition of operation, and the sweep moves downwardly in response to wave portion 154.

It is thus apparent that in response to each pulse from photocell 42, the sweep direction is changed so that the triangular wave of Fig. 6g is derived.

Clipper 128 is biased in a well-known manner to pass the negative portions of the triangular wave of curve 6g, below a reference line 155 to derive the square wave 156 represented in Fig. 6h. By applying the latter wave to low-pass filter 129 a voltage is derived which represents the relative position of reference point P" between the adjacent curves 21. This voltage is additively combined in adder with the voltage stored in counter 131 and the resultant is supplied to indicator 132. Accordingly, interpolated values of the dependent variable are obtained.

It is apparent that the cycle of operation just described, including positive and negative undulations 141 and 142 of the curve Fig. 6b, is repetitive.

While a particular number of sweeps, following initiating pulse 148, have been illustrated as occurring during the interval of wave portion 142 (Fig. 6b), obviously a greater number may be employed for increased accuracy. However an odd number of pulses should follow each initiating pulse during interval 142 so that multivibrator 121 is always in a given condition at the end of interval 142.

Although the invention has been described in connection with a computer for determining the value of a function of two independent variables, it may be usefully employed in other applications. For example, the vernier portion of the system may be employed as a curve follower in which it is desired to maintain the position of the spot on the face of cathode ray tube 30 of Figs. 1

or 2 between two curves. In this connection, a wellknown form of feedback system may be provided to control the position of the spot during intervals other than the occurrence of the vernier sweep so as to maintain the desired positional relationship.

Alternatively, the system may be employed to measure the spacing between adjacent curves. For this purpose, the two voltage undulations representing the position of the reference point relative to each of the curves may be suitably combined.

While particular embodiments of the present invention have been shown and described, it is apparent that changes and modifications may be made without departing from this invention in its broader aspects. Therefore, the aim in the appended claims is to cover all such changes and modifications as fall within the true spirit and scope of this invention.

I claim:

1. In computing apparatus including a screen having at least two indicia and means for projecting a beam of radiant energy toward said screen, an interpolation system for determining the position of said beam relative to said indicia comprising: means for displacing said screen and said beam relative to one another along a given path from a selected point on said screen in a first direction toward one of said indicia and in a second direction toward the other of said indicia; means responsive to the interception of said beam by said indicia for deriving electrical signal undulations representing the amount of relative displacement of said beam from said selected point to each of said indicia in each of said directions; and means for deriving indications responsive to said undulations of said electrical signal.

2. In computing apparatus including a screen having at least two indicia in the form of curves representing a function of two independent variables and means for projecting a beam of radiant energy toward said screen, an interpolation system for determining the position of said beam relative to said indicia comprising: means responsive to two independently variable quantities for determining a position of said beam relative to said screen; means for displacing said beam relative to said screen along a given path from said position in a first direction toward one of said indicia and in a second direction toward the other of said indicia; means responsive to the interception of said beam by said indicia for deriving electrical signal undulations representing the amount of said relative displacement from said position to each of said indicia in each of said directions; and means for deriving indications responsive to said undulations of said electrical signal.

3. In computing apparatus including a screen having at least two indicia and means for projecting a beam of radiant energy toward said screen, an interpolation system for determining the position of said beam relative to said indicia comprising: means for displacing said screen and said beam relative to one another along a given path from a selected point on said screen in a first direction toward one of said indicia and in a second direction toward the other of said indicia; photoelectric means for intercepting said beam subsequent to impingement on said screen to develop an electrical pulse signal in response to the interception of said beam by said indicia; means responsive to movement of said beam from said selected point and to said electrical pulse signal for deriving electrical signal undulations representing the amount of said relative displacement from said selected point to each of said indicia in each of said directions; and means for deriving indications responsive to said undulations of said electrical signal.

4. In computing apparatus including a screen having at least two indicia and means for projecting a beam of radiant energy toward said screen, an interpolation system for determining the position of said beam relative to said indicia comprising: means for displacing said screen and said beam relative to one another at a fixed rate along a given path from a selected point on said screen in a first direction toward one of said indicia and in a second direction toward the other of said indicia; means responsive to the interception of said beam by said indicia for deriving electrical signal undulations having a duration representing the amount of said relative displacement from said selected point to each of said indicia in each of said directions; and means for deriving indications responsive to the duration of said undulations of said electrical signal.

5. In computing apparatus including a screen having indicia in the form of a family of curves representing a function of two independent variables, means for projecting a beam of radiant energy toward said screen, and means for controlling said screen and said beam in accordance with two independently variable quantities to derive a first potential representing an approximation of the instantaneous value of said function for a point on said screen intermediate a pair of said indicia, an interpolation system comprising: means for displacing said screen and said beam relative to one another along a given path from said point in a first direction toward one of said indicia and in a second direction toward the other of said indicia; means responsive to the interception of said beam by said indicia for deriving electrical signal undulations representing the amount of said relative displacement from said point to each of said indicia in each of said directions; means for deriving a second potential responsive to said undulations of said electrical signal; and means for combining said first and said second potentials to obtain the instantaneous value of said function.

6. In computing apparatus including a screen having at least two indicia and means for projecting a beam of radiant energy toward said screen, an interpolation system for determining the position of said beam relative to said indicia comprising: means for displacing said screen and said beam relative to one another along a given path from a selected point on said screen in a first direction toward one of said indicia and in a second direction toward the other of said indicia; pulse generating means for deriving a first pulse initiated with the relative displacement between said screen and said beam in said first direction and terminating upon the interception of said beam by one of said indicia and for deriving a second pulse initiated with the relative displacement between said screen and said beam in said second direction and terminating upon the interception of said beam by the other of said indicia; and means for utilizing said first and said second pulses.

7. In computing apparatus including a screen having at least two indicia and means for projecting a beam of radiant energy toward said screen, an interpolation system for determining the position of said beam relative to said indicia comprising: means for displacing said screen and said beam relative to one another along a given path from a selected point on said screen in a first direction toward one of said indicia and in a second direction toward the other of said indicia; pulse generating means for deriving a first pulse initiated with the displacement between said screen and said beam in said first direction and terminating upon the interception of said beam by one of said indicia and for deriving a second pulse initiated with the displacement between said screen and said beam in said second direction and terminating upon the interception of said beam by the other of said indicia; and time-integrating means coupled to said pulse generating means for deriving a first potential having a magnitude representing the duration of said first pulse and a second potential having a magnitude representing the duration of said second pulse; and means for combining said potentials to obtain a third potential representing the position of said point with respect to one of said indicia.

8. In computing apparatus including a screen having at least two indicia and means for projecting a beam of radiant energy toward said screen, an interpolation system for determining the position of said beam relative to said indicia comprising: means for displacing said screen and said beam relative to one another along a given path from a selected point on said screen in a first direction toward one of said indicia and in a second direction toward the other of said indicia; photoelectric means for intercepting said beam subsequent to impingement on said screen to develop an electrical signal having a pulse representing the interception of said beam by one of said indicia; first and second bistable multivibrators individually having a pair of input circuits; means for supplying a pulse to one input circuit of said first multivibrator concomitantly withmovement of said beam relative to said screen from said point in said first direction and for supplying a pulse to one input circuit of said second multivibrator concomitantly with movement of said beam relative to said screen in said second direction; means for coupling said photoelectric means to the remaining input circuits of said multivibrators whereby said first multivibrator derives a first pulse initiated with the displacement between said screen and said beam from said point in said first direction and terminating upon the interception of said beam by one of said indicia and said second multivibrator derives a second pulse initiated with the displacement between said screen and said beam from said point in said second direction and terminating upon the interception of said beam by the other of said indicia; and means for utilizing said first and said second pulses.

9. In computing apparatus including a screen having at least two indicia and means for projecting a beam of radiant energy toward said screen, an interpolation system for determining the position of said beam relative to said indicia comprising: sweep means for displacing said screen and said beam relative to one another and responsive to the interception of said beam by said indicia for deriving a first sweep producing relative displacement from a selected position on said screen in a first direction and terminating at one of said indicia and a second sweep extending from said selected position in a second direction and terminating at the other of said indicia; and means responsive to said first and said second sweeps for deriving an electrical signal representing the relative position of said selected point with respect to said indicia.

10. In computing apparatus including a screen having at least two indicia and means for projecting a beam of radiant energy toward said screen, an interpolation system for determining the position of said beam relative to said indicia comprising: sweep means for displacing said screen and said beam relative to one another and responsive to the interception of said beam by said indicia for deriving a square wave having first and second time portions and for deriving a first sweep corresponding to said first time portion of said square wave produc-. ing relative displacement from a selected position on said screen in a first direction and terminating at one of said indicia and a second sweep corresponding to said second time portion of said square wave extending from said selected position in a second direction and terminating at the other of said indicia; and an integrator responsive to said square wave for deriving an electrical potential representing the relative position of said selected point with respect to said indicia.

11. In computing apparatus including a screen having at least two indicia and means for projecting a beam of radiant energy toward said screen, an interpolation system for determining the position of said beam relative to said indicia comprising: a bistable multivibrator having a pair of input circuits for controlling the conductive conditions thereof and a pair of output circuits for deriving at least one square wave having first and second time portions dependent upon successive changes in said conductive conditions; a sweep generating circuit coupled to one of said output circuits of said multivibrator for producing a sweep wave to displace said beam relative to said screen from a selected point on said screen intermediate said indicia; a discharge circuit having an output circuit coupled to said sweep generating circuit and having an input circuit; photoelectric means for intercepting said beam subsequent to the impingement of said beam on said screen to develop an electrical signal having a pulse representing the interception of said beam by one of said indicia; means for coupling said photoelectric means to said pair of input circuits of said multivibrator and to said input circuit of said discharge circuit whereby said sweep wave includes a first sweep producing displacement of said beam from said point in a first direction and terminating at one of said indicia and a second sweep producing displacement of said beam from said point in a second direction and terminating at the other of said indicia; and means responsive to the square wave at one of said output circuits of said multivibrator for deriving an electrical signal representing the relative position of said selected point with respect to said indicia.

No references cited.

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