Precision Parameters: Understanding PV and RMS Values

Bena Optics' Off-Axis Parabolic (OAP) mirrors are segments of parent parabolic mirrors, serving as primary mirrors. They are designed to achromatically focus collimated beams or divergent sources, with the off-axis configuration separating the focal point from the rest of the beam path. This reflective design eliminates phase delays and absorption losses typically introduced by transmissive optics, making OAP mirrors particularly suitable for femtosecond pulse lasers. As such, they are often used in constructing terahertz and infrared optical systems.

The substrate material for Bena Optics’ OAP mirrors is aluminum, processed with precision metal tooling to create surfaces that meet the highest standards and satisfy most customer demands. Our OAP mirrors feature key precision parameters, including surface accuracy, surface roughness, and surface quality. These parameters play a critical role in defining the performance and quality of the mirrors.

Surface Accuracy (PV and RMS)

PV (Peak-to-Valley)
Surface accuracy is determined by the "height difference" between the highest and lowest points on the mirror’s reflective surface. The term PV refers to the difference between the peak and valley of the wavefront error across the effective optical surface:
PV = Wₘₐₓ - Wₘᵢₙ
Here, Wₘₐₓ and Wₘᵢₙ represent the maximum and minimum values in the surface error matrix W(x, y), where x and y are the row and column indices of effective surface elements.

A PV value below λ/2 is generally considered high precision. Bena Optics’ OAP mirrors offer superior precision, with PV values ranging from λ/8 to λ/4, reflecting the excellent quality of our products.

RMS (Root Mean Square)
To understand RMS, it’s helpful to distinguish it from variance (Var) and standard deviation (STD). Their respective formulas are as follows:

1. RMS Formula:
   

   

2. Variance (Var) Formula:
   
   

3. Standard Deviation (STD):
   
   

Here, W(x, y) is the surface error matrix, N is the total number of effective surface elements, and \overline{W} is the average value of all effective elements.

• RMS is influenced by the average surface error value, meaning it reflects variations before or after piston removal.

• STD and Var account for deviations from the mean and are unaffected by the average value, focusing instead on the degree of surface flatness. Smaller STD or Var values indicate a smoother surface.

• STD is the square root of Var.

In optical terms:

• PV measures the difference between the highest and lowest surface points.

• RMS represents the average deviation of surface irregularities.

For high-quality optics, a PV of 0.1λ generally corresponds to an RMS value of approximately 0.02λ, with PV values typically 3 to 6 times greater than RMS. Some vendors may claim λ/8 or λ/10 precision, referring to RMS, while their PV may fall short of 0.5λ. A genuinely high-precision optical component should ideally have a PV value of at least λ/2.

Bena Optics offers OAP mirrors with RMS values better than λ/8. By comparison, our competitor Thorlabs provides OAP mirrors with RMS surface accuracy (also called RWE, or Reflective Wavefront Error) values of λ/4 or λ/2 (λ = 633 nm). This comparison highlights the strong competitive position of Bena Optics in the domestic and international markets for high-precision OAP mirrors.