## 1 Introduction
[28] proposed the concept of image deformation, in which the interrogation window is deformed according to the kinematics formula to improve the calculation accuracy in a complex flow state. [PERSON] and [PERSON] [29] adopted a Taylor expansion to fit the displacement distribution in the deformation algorithm and combined it with an iterative multigrid algorithm to create the window deformation iterative multigrid (WIDIM) algorithm, which is now widely accepted. To reduce the amount of calculation, [PERSON] [30] used bilinear interpolation to construct the pixel point displacement field for image deformation. [PERSON] [31] analyzed the bilinear, shift bilinear, B-spline, and FFT interpolation methods. The B-spline method has the highest interpolation accuracy, and the second-order B-spline can be applied to most actual scenarios. Figure 1: Principle of digital particle image velocimetry (DPIV) technology: (**a**) the velocity calculation method and (**b**) DPIV system. There are still many limitations in multiphase flow measurement by DPIV, such as the shielding of oil against tracer particles in oil-water two-phase immiscible flow [32]. [PERSON] et al. [33] applied DPIV to the small diameter horizontal oil-water two-phase immiscible flow with oil droplets as tracer particles, and the results represented the average accumulation flow velocity of oil droplets in the shooting direction. [PERSON] et al. [34] applied DPIV to oil-water two-phase immiscible flow in a small diameter horizontal well, and modified the window overlap method in the WIDIM algorithm to improve the measurement accuracy. Although these algorithms are effective in their application filed, they do not perform well for oil-water two-phase immiscible flow measurement in an inner diameter 125 mm vertical upward pipe. The inner diameter 125 mm vertical well is the most widely used in oilfields. At low flow velocity and high water cut (the water volume percentage), water is the continuous phase and oil is the dispersed phase and the fluid appears as the bubbly flow state in the well. Oil droplets are small in inner diameter 125 mm vertical upward pipe, with good follow ability, and could be used as tracer particles to obtain the shooting direction cumulative average flow velocity distribution information in the plane. At present, the following problems exist in the application of the WIDIM algorithm in DPIV to oil-water two-phase immiscible flow velocity field measurement in an inner diameter 125 mm vertical pipe. (1) As a result of the large diameter, the relative motion range of oil droplets in the interrogation window is very large. Therefore, the following performance of the interrogation window is required to be good enough. However, the following performance of the interrogation window does not meet the demand of the velocity measurement of 125 mm vertical upward oil-water two-phase immiscible flow. (2) Compared to small-scale laboratory investigations, the larger spatial domain increases the illumination issues and oil droplets shielding problems, especially if the LED source is placed behind the pipe. (3) Because the application object of DPIV is two-phase flow with oil tracers, the gray image of two-phase flow is more complex than that of single-phase flow. This makes the cross-correlation calculation prone to mismatching and generating plenty of false vectors so as to leads to the measurement error. The error may be amplified during the iteration process of the algorithm,  
Figure 2: Particle motion in interrogation area: (**a**) particles run out the interrogation window, (**b**) particle motion with large velocity, and (**c**) window deformation. especially the initial calculation error, thereby seriously affecting image deformation performance. Hence, the iteration calculation accuracy should be improved as far as possible; thus, the method how to increase the accuracy of the iteration calculation should be studied.