the instrument illustrated in fig1 and 2 includes the upper housing section 10 , the lower housing section 11 , a translucent table panel 12 , and an overarm 13 . this cantilever member supports the detector unit 14 positioned directly above the opening 15 in the panel 12 . the elevated portion 16 of the housing supports a front panel 17 providing an opening 18 for the window 18a through which the digital readout 19 is visible . the panel 17 also has openings for the control 20 of an off - on switch , and for the control 21 providing a null adjustment for the instrument . the cantilever overarm 13 is part of a u - shaped structure indicated generally at 22 in fig2 with a base portion 23 normally secured to the bottom of the light box 24 attached to the bottom section 11 of the housing . screws as shown at 25 and 26 traverse appropriately located holes in the bottom of the light box , and engage the lateral flange portions of the base 23 , as shown in fig2 . the base 23 is assembled to the light box through the opening 27 , and the integral construction of the member 22 assures the proper alignment of the test light 28 secured to the base section 23 of this member . this light , and the detector unit 14 , may be considered as coaxial with the hole 15 in the translucent panel 12 . wiring as shown at 29 associates the test light 28 and the detector 14 with the principal circuitry of the instrument mounted on the printed circuit panels 30 and 31 , together with the power provided through the exterior power cable 32 . the panel 30 is mounted in the elevated section 16 of the housing , with the digital readout elements 19 in proper position for registry with the window 18 . in addition to the arm assembly 22 , the light box 24 contains the fluorescent tubes 33 and 34 supported between the usual brackets as shown at 35 - 37 fastened in the usual manner to the walls of the light box 24 . conventional ballast assemblies as indicated at 38 and 39 are incorporated for association with these fluorescent tubes . light from these tubes provides a general field of illumination underneath the translucent panel 12 , so that a sample of film can be placed on this panel underneath the arm 13 for a general inspection of a photographic film , preparatory to selecting a particular area for placement directly under the detector 14 . a transformer as shown at 40 is associated with the circuit supplying power to the test light system , derived from the incoming power cable 32 through the conventional assembly of fuses and connectors indicated generally at 41 . the assembly indicated at 42 provides a clamping receptacle for the wire harness within the housing section 11 that electrically associates these components . the remaining items appeared in the exploded view of fig2 are standard fastenings and devices shown in positions projected from their assembled relationship . the nameplate sections 17a and 17b may be considered as part of the panel generally indicated at 17 in fig1 . these may be integral , or separated as shown . referring to fig3 the light unit 28 includes the bulb 43 having the base 44 fixed with respect to the section 23 of the arm assembly 22 . the tubular extension 45 positions the lens 46 for collimating the light from the source 43 , which is projected through the aperture plate 47 , and then through the film sample 48 . the detector , or light sensor , 14 receives whatever light traverses the film 48 , and provides a response signal delivered to the measurement system indicated schematically at 49 in fig3 . the annular rubber seal 50 is incorporated to block off light from surrounding sources , as well as confine the light traversing the film 48 . a color filter 51 is preferably incorporated in the assembly , and retained between the member 23 and the extension 45 . light emerging from the filter 51 may be considered as the test light source . a part of this light proceeds through the lateral passage 52 , and is received by the sensor - detector 53 as a reference light beam , with the response of the sensor 53 to this beam being delivered to the measuring system 49 to compensate for variations in the intensity of the bulb 43 . the light tranversing the film 48 may be considered as the test beam , which is monitored in conjunction with the reference beam to provide a compensated indication of the density of the film sample 48 . referring to fig4 the output of the detector 14 is applied to the input terminals of the operational amplifier 54 , the output of which is applied to the base terminal 55 of the matched - pair transistor unit generally indicated at 56 . the opposite base terminal 57 is grounded , as shown . the collector terminal 58 is directly connected to the point 59 associated with the input lead of the operational amplifier 54 . the second operational amplifier 60 receives the output of the reference sensor - detector 53 , with the output of this amplifier being supplied to the emitter terminal 61 of the matched - pair transistor 56 . the capacitors indicated at 62 and 63 limit the high frequency gain of the operational amplifiers to prevent oscillation . the resistor 64 limits the maximum current into the matched - pair of transistors , and controls high frequency gain . the operational amplifier 54 functions in feedback relationship , as a result of the connection through the capacitor 62 , the lead 65 , and the lead 66 . the current from the detector 14 is indicated at 67 , and the effect of the circuit relationships involving the operational amplifier 54 and the matched - pair transistor 56 is to cause the measurement - indicating voltage at 68 to respond to satisfy the requirement that the currents indicated at 67 , 69 , and 70 should equal zero with respect to the point 59 . the characteristic of a matched - pair transistor is that a logarithmic voltage impressed across the two base leads produces a linear collector current response . if the current 67 increases by a given amount , the operational amplifier senses the imbalance between the current 67 and the current 69 , and drives the voltage at 68 more negative . the differential voltage across the matched - pair transistor is then increased by ## equ1 ## this causes the collector current i 71 to increase by δi 71 until δi 71 = δi 67 . the voltage required to generate δi 71 is : ## equ2 ## the output ( readout ) voltage at 68 is thus a logarithmic function of i 75 / i 71 . operational amplifier 60 controls the total current through both sides of the matched - pair transistor 56 , which is approximately the total of the currents 71 and 72 . if the current 71 is increased , then the current 73 includes the currents 71 and 72 , together with the amount of the increase in the current 71 , so that the sum of the currents at the point 74 shall remain equal to zero . with this arrangement , if the current 75 from the reference sensor 53 increases , both sensors will produce an equal percentage of increased current . the logarithmic relationship of the readout voltage at 68 is thus unaltered , as is indicated by the following : where k is a constant , expressed in volts , relating amplifier output to the logarithm of the current ratios . thus , although the above discussion concerns transmission densitometry , it also applies to relection densitometry .