Constructing an image analogous to that, which could be seen if visible radiation could penetrate the object that is main goal of nondestructive inspection by using ultrasonic wave [1]. The resolution of all imaging system is limited by effective aperture size over which data can be collected. The SAFT was developed to overcome limitations in fabricating and controlling the large physical aperture to improve the resolution, which is necessary in the conventional imaging technique [2]. SAFT processing is just simulating a focused transducer, which is performed in computer software [3]. Fundamental SAFT equation is:
 (1) 
Where, N is the number of transducers, X_{n} represent the signal received by nth transducer, c is the velocity of the sound in the media and r_{n} is the distance between transmitter and nth transducers [4]. When high frequency waves are used for inspection this formula works properly. For inspecting some materials such as wood and concrete, which highly attenuate ultrasonic waves the high frequency can not be used, therefore this formula can not be used directly. Very low frequency (about 100KHZ) probes inspect these kinds of material. Very low frequency probes have two characteristics, which are arise problem in using above formula. They are long ringing time and large diameter of transducers. Because of long ringing time, any sample in recorded data can not be considered as a value which is measured reflection of ultrasonic wave from points in same distance of transmitter and receiver. Large diameter of transducer reduces the resolution, which is one of the main objects of SAFT algorithm.
In this work by using geometrical mean of root mean square (RMS) value and maximum of the reflected signal the area of reflection and the amount of reflecting ultrasonic signal is translated in one number. These preprocessed data are used in SAFT algorithm.
In pulse echo method one transducer is used for transmitting and receiving ultrasonic waves. Fig. 2 shows a typical received signal. This signal is completely corrupted by noise. For removing this noise from signal averaging method is used. In each point 256 times data is collected and average of them is considered as receiving data to that point. Fig 3 shows the noiseless data with this method. In this figure "a" shows the reflection from first contact area between transducer and outer world, "b" indicates reflection from flaw(s), "c" is reflection from back wall and "d" is repetition of "b". If more data is acquired the other area are repeated. In using SAFT algorithm must be aware of this redundancy data, otherwise wrong result may be obtained. The central frequency of probe is 125KHZ with 75KHZ bandwidth. Based on sampling frequency theorem the frequency
of sampling analogue signal must be greater than or equal two times of the biggest frequency, which is exist in the signal.
Fig 2: Noisy data

In here another criteria must be considered. The recorded data is based on time but by using velocity of ultrasound in media the time axis can be translated to the place. In recorded data between two samples there is a time difference equal 1/f_{s} in which f_{s} is sampling frequency. When time axis is translated to place axis, between two samples there is c/ f_{s} distance. It means the vertical resolution depend on ultrasound velocity and sampling frequency. For a specific material the velocity can not be changed. Therefore more resolution needs higher f_{s}. The 2MHZ sampling frequency is used in this work.
Fig 3: Data without noise

Different flaws are considered for comparing different constructing imaging system. At first time two flaws are choose, which are one rectangle 20x24x3 mm and one disk with 13mm diameter and 3 mm thick. These two flaws are put in different distance, 40, 20 and 2 mm. The second test is held by putting above two flaws and two different rectangle 30x18x2 mm and 20x20x2 mm. In third test a disk by 40mm diameter and 5 mm thick is used. Different size and configuration of flaws are considered to provide a complete discussion about different methods.
Constructing images by using conventional SAFT
The following images are reconstructed by using equation one.
Fig 4: a) Two flaws in 4cm distance b) Two Flaws in 2cm distance c) Four flaws 
As the images show there is nothing clear on them. This situation is happen because the locus of the points, which are in same time delay, is a spherical. The time ringing of the transducer is long therefore for one reflected point in different delay the same grey level is repeated.
Constructing image by new method
Reflected signal has two characteristics. They are maximum value and duration time of reflected signal from flaw. These two can be used for determining the area of reflection. Geometric mean of root mean square (RMS) value of signal and maximum of it is considered as a value. This value is used for determining the grey level and area of reflection. When transducer is moving this area is move and different area with different grey level are add together. The result of this summation is an image, which shows the shape of flaw. Fig 5 shows the result of preprocessing data for different position size and number of flaws.
In Fig 5 the x axis shows the file number, y axis shows scan line number and z axis shows the geometrical mean of RMS value and maximum value of signal in that point. In a and b distance between each point is 3mm and the aperture cover completely the flaws. It can be seen the number of flaws and the position of them can be estimate from this preprocessed data. In c the distance between each point by previous one is 1 mm and the aperture can not cover the whole flaw, as it shows in diagram. When the transducer is over the flaw maximum reflection is happen. For finding the flaw this fact is used. First step in calculating flaw image is started from this point. For the probe, which is used in this experiment 0.1 of the maximum value is good estimate for the area, in which flow can be existed. In second step, a grey level equal the measured signal in that point to all point inside a circle is assigned. Centre of this circle is in the same position of probe centre. This process is continued for all other probe positions, which are inside the estimated area. When the process is over an estimated area is finished, other maximum is used and this process is repeated for new area. The results of this method for different flaws are shown in Fig 6. Characteristics of flaws are described in previous section.
Fig 6: Flaw images by new method: a,b,c) Two flaws, d) Four flaws and e) One big flaw as describe in section 3.

Each image shows a 150x200mm area. In Fig 6 left image is reconstructed by new algorithm and right image is processed image by edge detection.
Reconstructing image by cscan method
In this method maximum of recorded data is considered as reflection from the point, which is in the same position under transducer. It can be seen in this method the shape of the flaws can not be found clearly.
Fig 7: Flaw images by Cscan method: a) Two flaws, d) Four flaws and e) One big flaw.
