Study of a Photodetector for a Densitometric Complex Characteristics
So, the National Institute of Standards and Technology of the USA (NIST) has developed the instrument of optical density measurement in transmitted light of standard samples SRM 1001 and SRM 1008 which represent the step optical attenuators on X-ray and photographic films. The optical density measurement instrument allows estimating the diffuse optical density within the range up to 6 B and the standard uncertainty is equal to 0.002 B, expanded uncertainty (when coverage factor k = 3) is equal to 0.006 B [1-3]. Thermally-stabilized photodetector (PD) which consists of silicon photodiode and preamplifier is the basis of the measurement device. PD ensures the measurement of optical signal within the range of seven orders of magnitude and for this reason the range of transmission optical density is extended up to 6 B.
In order to study the linearity of PD in the structure of reference reflectance spectrophotometer the double aperture method  can be used or when measuring the densities of more than 3 B the diagram of current conversion into voltage can be used with its further amplification . The absolute error of optical density measurement of less than ±0.005 B was obtained in the designed densitometer .
However, the papers [1-6] have one shortcoming, they do not have the description of estimation methods of the PD key parameters – sensitivity, dynamic range and linearity. But these specific key parameters determine the quality of measuring systems which PDs are built in.
Analysis of the leading published papers [1-6] showed that PDs used for the measurement of visual diffuse optical density with high accuracy were made on the basis of silicon photodiode and with transimpedance amplifier which converts the photodiode current into the output voltage of operational amplifier. Switching over of the resistors in the feedback of preamplifier ensured the dynamic range of PD operation.
In our paper the PD made according to the diagram of integrator rather than transimpedance amplifier was used as the detection system of densitometric complex. The PD under study consisted of spectrophotometric detector СФД-1 and controller. The detector СФД-1 included silicon photodiode  with the active region diameter of 10 mm designated for the registration of radiation within the spectral range 200-1180 nm. It had the temperature coefficient of external quantum efficiency of 0.01%/ºС for the wavelengths 885–238 nm . Besides the silicon photodiode, the detector СФД-1 included photodiode current converter assembled in accordance with the integrator diagram. The detector СФД-1 was made in the form of hybrid assembly and registered the current signals on one measuring element within the whole dynamic range . The output signal from СФД-1 in the digital form is poorly exposed to the external electromagnetic disturbance. Controller provides the processing of digital data obtained from the detector СФД-1 and transmission of the measurement results to the personal computer (PC). Software designed for the PD under study provides the record and processing of data which comes from the controller as well as the graphic display of measurement results (Fig. 1) of PD based on the detector СФД-1. The detector СФД-1 dimensions: diameter – 20 mm, and height – 10 mm. СФД-1 conversion coefficient was estimated using the source of calibrated direct current which was made on the basis of AD581 reference voltage sources and precision wire-wound resistor. Check up of the calibrated current source is given in Table 1.
Within the framework of this paper the optical signals within the spectral range 350-1100 nm were registered by the silicon photodiode. Photocurrent measurements were performed at the temperature 20-25°С.
The diagram of PD relative spectral sensitivity obtained on the basis of calibration results in All-Russian Research Institute of Optical-Physical Measurements, Federal State Unitary Enterprise (ARIOPM FSUE) on the Higher-Accuracy Device for the reproduction of spectral sensitivity units within the range of wavelengths 0.22-2.5 µm (УВТ 42-А-86) is shown in Fig. 2.
Study of Dynamic Range and Linearity of PD Energy Characteristic
In order to determine the applicability of investigated PD as the photodetector unit in the structure of densitometric complex the following measurements were performed: measurements of noise parameters, dynamic range and linearity of energy characteristic of investigated PD.
Optical Scheme and Equipment
Study of noise parameters, dynamic range and linearity of energy characteristic of investigated PD was performed on the device optical scheme of which is shown in Fig. 3. The photometric incandescent lamp of СИРШ 8.5 – 200-1 type (voltage 8 V, current 23 A) was used as the radiation source, the photodetector СФД-1 based on silicon photodiode and integrator was used as the radiation-measuring instrument. Power was supplied to the lamp СИРШ 8.5 – 200-1 (2) by the stabilized power source СИП-30 and in order to control the lamp voltage the voltmeter В7-54/3 was used. Lamp voltage which was supported by means of the P33 resistor bank was equal to 8.0020±0.0004 V. PD voltage which was estimated by means of the MPS 3020 stabilized power source was equal to 6.00±0.01 V.
Method of Study
The method of measurement of photoelectric parameters and estimation of PD characteristics was taken as the basis of the study . The point of this method lies in the determination of relation between two magnitudes of photodetector current intensity: one magnitude occurs when the luminous flux falls on photodetector, other magnitude occurs when the light falls on photodetector upon absence of the sample under study. Variation of luminous flux which falls into the integrating sphere was performed by three different methods: first of all, changing the distance between light source and integrating sphere; secondly, diaphragming the luminous flux; thirdly, introducing the neutral filters into the optical path. And combination of these methods with the different compositions of optical elements made it possible to change the intensity of luminous flux which fell into the integrating sphere within wide range. Upon each combination of optical elements and registration of dark current the signal measurements were performed by the series consisting of 10 observations (period of one observation was 3 s) and the mean value Ī was estimated as well as mean square deviation of measurement result S in accordance with the standard methods .
Estimation of the Dynamic Range
Estimation of the dynamic range was performed on the basis of the method established in the paper . Dynamic range was estimated according to the following formula:
Д ≤ Iф ∙ КФ / IП, (1)
where IФ stands for the photosignal current, КФ stands for the attenuation coefficient of the filter introduced into optical path, IП is the value of noise current, in other words, photocurrent which corresponds to the threshold of sensitivity ФП.
Estimation of Noise Current Which Corresponds to PD Threshold of Sensitivity
PD noise current value was estimated when the installed screen (see Fig. 3) was blocking the way of luminous flux to the access port of integrating sphere. At this moment the total current Iобщ and dark current IT were being registered in the PD output. According to the results of their measurements using the designed software the value of photocurrent was being calculated according to the formula IФ = IОБЩ – IT. The photocurrent value IП corresponding to the threshold of sensitivity ФП of detector was assumed as the current value which is equal to IП = 3.25SШ, where the coefficient 3.25 stands for the Student’s coefficient with the confidence coefficient P=0.99 and SШ stands for the mean square deviation of the measurement result of mean dark current ĪТ. As a result of measurements the photocurrent value IП was estimated which corresponded to the threshold of PD current sensitivity, IП = (1.9 ± 0.2)∙10-5 nA ~ 2∙10-5 nA.
Then, varying the distance between the source and integrating sphere (L1=300 cm, L2=157 cm, L3=80 cm, setup error 0.1 cm) we changed the luminous flux falling into the integrating sphere. Luminous flux was directed straight on the diaphragm Д (see Fig. 3) and the filters НС11, НС13 were introduced on the way of beam. 4 different diaphragms with the following diameters were used: Д1=1.3 mm; Д2=4.0 mm; Д3=12.0 mm; Д4=40.0 mm.
Results of the first and second series of measurements of the photocurrent IФ are given in Table 2 upon the different combinations of optical elements in the optical scheme. Results are arranged in decreasing order from the maximum value to the minimum one: from Imax=1283.540 nA to Imin=0.000060 nA – for the 1st measurement series; and from Imax=6328.193 nA to Imin=0.000087 nA – for the 2nd measurement series. Thus, the range of detector measured currents in the first measurement series is Imax/Imin=1283.540/0.000060=21392334.3~2.1∙107 and LOG10 (Imax/Imin)=7.33±0.06; in the second measurement series Imax/Imin = 6328.193034/0.000087 = 72737850.97~7.3∙107 and LOG10(Imax/Imin)=7.86± 0.07.
The dynamic range Д when IФ=Ī=647.3 nA (Table 3, 3rd row of the 2nd measurement series), КФ=9.78 and IП = 0.00002 nA obtains the following value Д = 3.16530∙108, and LОG10Д = 8.50 ± 0.07.
Study of Linearity of PD Energy Characteristic
The method  was used for the study of linearity of energy characteristic. According to the results of photocurrent measurements (Table 2) and taking into account the known values of transmission coefficients of elements introduced into the luminous flux (optical filters, diaphragms, variation of distance between the light source and integrating sphere) the analysis was carried out. It showed that the error of optical density estimation concerning these elements does not exceed 0.2% within the range of measured currents of the PD under study (from 0.006174 nA to 6328.193 nA in the 2nd measurement series).
The results obtained during experiments indicate that the energy characteristic deviation from linearity by the criteria specified in the paper  does not exceed 1% within the range Д=4.1∙106. In the logarithmic scale the energy characteristic deviations from linear law do not exceed 0.003 B within the range 0.03 – 6.6 B.
Study of Linearity of the PD Energy Characteristic Using the Method of Double Aperture
The linearity of PD energy characteristic was studied additionally using the double aperture method  within the spectral range (340-770 nm) given in the document . Luminous flux from the lamp after passing the filter Ф1, neutral filter ФН, diffuser and diaphragm (with diameter of 3 mm) was falling on the non-transparent mask which had two openings А and Б (with diameter of 1 mm). Openings were located in such a way that both of them were inside of the area covered with this diaphragm and the distance between their endpoints was 0.4 mm. The scheme of PD linearity study via the double aperture method is described in Fig. 4. Radiant flux coming from these openings was blocked by the door. The door was installed on the holder which was actuated mechanically by the stepping motor. In such manner the light could be blocked from one opening A or Б by the door or from two openings simultaneously. The spectral characteristic of luminous flux falling on the diaphragm determines the lamp radiation spectrum and filter Ф1. It corresponded to the spectral conditions of optical density measurement in the transmitted light according to ISO 5-3 .
Use of the neutral filters ФН set the levels of intensity of transmitted radiation, their values changed within the range of 7 orders. Spectral characteristic of the elements located near the diaphragm was estimated by the filter Ф2 and spectral sensitivity of PD and corresponded to the spectral conditions of measurement of standard visual diffuse density in the transmitted light according to ISO 5-3 .
Photocurrent obtained upon the unblocked opening А or В was designated as SА or SВ. Current signal obtained with two unblocked openings was assumed as SА+В. Upon every level of radiation set by the neutral filters НС-3, НС-10 and НС-11 or their combination the series of measurements of signals SА, SВ and SА+В were performed. Analysis of ratio of the signal values SА/SА+В and SВ/SА+В showed that the ratios stayed constant with the relative error Ī of not more than 1% within the range of radiation intensity of 6.4 orders. Photosignal values were flattened at the negative peak by the photocurrent value IП ~2∙10–5 nA which corresponded to the threshold of photodetector sensitivity ФП. In other words, the study of linearity of the PD energy characteristic using the double aperture method confirmed that the results of measurements of PD energy characteristic linearity using the method  and double aperture method  correspond to each other.
Performed study of noise parameters, dynamic range and linearity of the PD used in the structural diagram of reference densitometer in the transmitted light (Table 3) confirmed the applicability of the PD based on silicon photodiode for the measurement of optical density within the dynamic range of more than 8 B.