To realize the flow visualization of shock train structures by Schlieren measurements in a square-to-circular transition isolator, a high-precision conformal optical window was manufactured by fly-cutting technology. According to the light refraction principle, the window's outer surface was iteratively optimized based on the super-elliptic curves of the internal flow channel. Through tolerance analysis and processing parameter optimization, the transmitted wavefront error (RMS value) of the finished window was 0.823λ (λ=632.8n m). Based on a z-type Schlieren apparatus, the high-precision Schlieren measurements were conducted through the window and processed by an image filtering process method. The results promote high-precision Schlieren observation towards square-to-circular transition isolators.