The key unit of the linear array is a module, consisting of 128 sensitive elements of gallium arsenide chromium doped resistive type material which was designed, manufactured and assembled in Siberian Physical-Technical Institute of Tomsk State University [9] [10] . The pitch size of a single element can be 100 × 100 μm² or 200 × 200 μm² and the sensitive length of material vary from 600 μm for pad elements up to 4 mm for strip elements. Figure 1 shows two detectors modules of strip sensitive elements with 200 μm pixel pitch, mounted on the printed circuit board. Arrows show the direction of photon flux. The maximum array length was 400 mm assembled from 16 modules. Due to technological reasons is it impossible to make all the modules with same sensitivity

to the x-ray exposure, moreover the sensitivity of pads and strips vary not only from one module to another but also inside each module. The transformation of signals from detectors into useful voltage signal is done by 128-channel ASIC chip [11] . Every channel of ASIC consists of: input circuit for matching of bias voltage of sensitive element, personal 8-bit compensation current generator and 8-bit storage memory, compensation current generator for all channels, integrator and buffer. ASIC output doesn’t have any programmable gain amplifiers to adjust the sensitivity of each element. That is the reason why we have to do a programmable software adjustment. The connection between sensitive elements and ASIC is made by ultrasound welding. The chip is converting the electron charges, formed by the x-ray flux into serial sequence of voltages.

There are two possibilities to control the output serial voltage signals of ASIC. The first one is to adjust the average level of output signals and the second one is to adjust input current for every sensitive element to minimize the spread of dark currents of all detectors on the module. To adjust both average level of output signals value and individual dark currents the chip has several analog and digital inputs. The adjustment of the mean level is controlled manually with the potentiometer and with the software regulations of the dark currents by writing 8-bit value codes in ASIC. These two possibilities allow control a shadow signals only when there is no x-ray flux.

For each sensitive element there is a transfer characteristic function of output voltage in dependence of input 8-bit code from 0 to 255. By calculation of optimal input codes (sometimes it’s called a mask) it is possible to get output serial voltage signals as a straight line. The current of each input of ASIC includes three components, they are: I_det-current formed by sensitive element under x-ray exposure, I₁-average current of all 128 sensitive elements, I₂-compensation current, k-input 8-bit value. The output voltage signal for every one is proportional to input current and clock frequency.

Clock frequency is constant during the exposure and acquisition. Voltage sequence transformed by ADC into counts has a form as it showed in a Figure 2.

The ADC count has three main ranges (3), two of them are constants, and one is the working range where the dark current can be compensated.

To make all signals have the same or close to same A_base count value it’s necessary to calculate N_base input value for each chip sensitive element input. To do that it’s necessary to form a response matrix A.

where m is number of input values in chip, and n is amount of sensitive elements. In our case the maximum m is equal to 255 and n is equal to 128. The m values could be an array of equidistant distribution with different step from 0 to 255, e.g. .

The easiest way to find the N_j = N_base or it nearest neighbor is to calculate the index of minimum absolute difference between A_base and each element of column vector A.

where

After finding all compensation values for the array and writing them into ASICs, in result the output voltage signal will be with minimum spread. If an equidistant distribution step not equal to 1 the Figure 3 shows the spread of ADC counts from a single module.

However, there is still a different sensitivity of detector elements to x-ray flux, even when all values for dark current compensation are correct and output signals without x-ray flux are a uniform. That pattern depends on many parameters such as bias voltage of detector elements, sampling clock frequency, high voltage of x-ray tube etc. To reduce such pattern we use a calibration test-object which has a shape of a ramp. The idea of sensitivity adjustment is based on a calculated response from a reference uniform signal for different intensities. Such shape allows to simulate the variation of x-ray flux intensity and get a response of each sensitive element under the same uniform x-ray flux. In our case the maximum difference in the ramp thickness is 20 mm that covers the major part of studies where x-ray high voltage is equal or less 70 kVp. Figure 4 demonstrates the ramp object scanned from top to bottom by the linear array with 5 detector modules. The data presented after dark current compensation. The vertical pattern represents the different sensitivity from one detector element to another.

For a typical x-ray tube that has a bremsstrahlung spectrum as well as characteristic lines, the mono-energetic formula of intensity attenuation like (6)

can’t be used to calculate the response of each sensitive element and compensate it, thus the response of each sensitive element is represented as a polynomial dependency (7), where d is a ramp thickness and k_i are coefficients, which allows to take into account both the scattering and absorption of x-ray photons.

Figure 5 shows, as example, a simulation of spectrum of the x-ray tube source with tungsten target, with 70 kVp anode voltage, and built-in 2.5 mm plus additional 20 mm aluminum filter. The spectrum generated with Monte-Carlo simulation program XMIM-SIM [12] [13] . The detector current response for such difference in intensity and x-ray energy is easier to describe as a polynomial expression.

To find the k_i coefficients we use the data of the ramp object exposure. The data of a raw image for sensitivity compensation is B, the ramp test-object is represented as a matrix R where each row is an array’s data on the same ramp thickness. The vector Z is the values proportional to dⁱ from (7). Number of rows in R and Z is the same.

In order to compensate the amplitude difference between all sensitive elements, we calculate an adjustment value for each pixel in B.

To compensate sensitivity of all elements to the same level we use a ramp as a reference

and for each raw image pixel we calculate a minimum index of the absolute difference between pixel and ramp matrix column. Column vector Y is formed for each element of matrix B.

As a result the compensated pixel will be

In order to increase a number of rows in matrix R the interpolation could be done by calculating additional data for all rows. Equations (11) and (7) allow to find k_i coefficients with linear least square approach and recalculate row data for expanded Z.

The resulted image formed from pixels, calculated from equation 10 is represented as “for processing” in DICOM 3.0 format for further PACS systems.