## 1 Introduction  
Whether it is in the high-end fields such as the defense industry, aviation and aerospace, or in the civilian fields of medical devices, mobile phones, cameras, etc., high-precision optical components are playing an increasingly important role. At the same time, there are increasingly higher requirements for surface form error, medium frequency error, surface roughness and subsurface damage of optical components [1]. With the introduction of aspherical and free form surface design methods, precision devices composed of optical components have been unified in terms of portability and functionality. However, this also poses a great challenge to the ultra-precision machining of optical components. Ultra-precision grinding and deterministic polishing are the main means of processing ultra-precisionoptical components [2]. Traditional manual polishing has the disadvantages of high labor intensity, poor working environment, being time consuming, high dependence on workers' experience, difficulty in controlling the consistency of quality, etc. [3]. Automated polishing is inevitably a trend to replace manual polishing. Computer-controlled optical surfacing technology (CCOS), first proposed by Itek. Inc. in 1970, has been widely used and developed in optical surfacing with high form accuracy [4; 5]. In recent years, with the development of a series of advanced non-traditional sub-aperture CCOS polishing technologies such as bonnet polishing [6], fluid jet polishing [7], magnetorheological polishing [8], ion beam polishing [9], laser polishing [10], etc., the controllability of deterministic polishing has taken a new step, which provides more possibilities for the improvement of the correction effect of the surface form error. Among them, fluid jet polishing is an ultra-precise finishing technology that combines fluid mechanics, precision manufacturing and surface engineering. In this polishing technology, the fluid is used as a carrier for the abrasive particles suspended within, forming a flexible polishing head that acts on the workpiece surface with a good fit and gets rid of tool wear issues altogether. Therefore, this technology has a strong adaptability to complex free form shapes and is especially suitable for the ultra-precision polishing of optical lenses, mirrors and molds made of hard and brittle materials. In addition, fluid jet polishing in the general submerged polishing case and some non-submerged polishing cases with narrow sapphire nozzles (with a diameter less than 0.3 mm) can generate tool influence function (TIF) with a small radius and a Gaussian or near Gaussian distribution. These advantages make fluid jet polishing a strong technology to achieve precise correction of the surface form error. In the technology of CCOS, the convergence of surface form error has a close relationship with the distribution of surface form error, calculation of dwell time, tool influence function (TIF) and path planning. In practice, after measurement of the workpiece to be polished, the resulting surface form error can be generally expressed as a continuously changing free form surface. The optimal distribution of residual error after deterministic polishing should be as close to an ideal plane as possible and ensure sufficient convergence accuracy. However, the distribution of surface form error directly brings a difference in bulk material removal depth across a to-be-polished surface in subsequent corrective polishing. After the surface has been polished with a traditional path with a fixed pitch, it can be seen that the residual error distribution after deterministic polishing is largely affected by the distribution of parent surface form error. In this paper, this phenomenon is identified as a genetic phenomenon of error distribution. This makes it difficult to ensure the consistency of the accuracy in the entire region of the workpiece after ultra-precision polishing, and it also brings difficulties for subsequent iterations of corrective polishing.