How Aspheric Surfaces Are "Forged"

How Aspheric Surfaces Are "Forged"​​

In two previous CAS’Tech class articles—"To distinguish between “aspheric” and “spheric”, why to make it “perfect”?"and "CASTECH's "Aspherical" Extraordinary Journey"—we introduced the basic concepts of aspheric lenses and highlighted CASTECH’s manufacturing capabilities and metrology equipment for aspheric surfaces. In today’s session, let’s step into CASTECH’s Aspheric Processing Center to take a deeper look into the precision machining of computer-numerical-controlled (CNC) aspheric lenses.

Principles of Precision CNC Machining for Aspheric Surfaces​​

Similar to traditional spherical cold processing, the precision CNC method also belongs to the Material Removal Process (MRP), which employs grinding, polishing, and other means to remove material from the workpiece surface. The key difference lies in the fact that precision CNC is built upon the digitization and quantification of theoretical assumptions and machining experience. A computer controls the relative movement of the tool along the ideal aspheric surface profile while performing highly localized (point or small-area) contact removal. This approach significantly enhances machining accuracy and repeatability.

Based on the principle of minimal material removal, we use the “best-fit sphere”—defined by the vertex and edge points of the target asphere—as the spherical blank. After removing the "excess" material, the blank is precisely "corrected" into the desired aspheric shape. Figure 1 illustrates the MRP-based aspheric machining process, with the red areas indicating the material removed:

Figure 1. Schematic diagram of machining aspherical surfaces using the MRP method

Clearly, the larger the aperture of an aspheric lens, the more material needs to be removed, and the longer the processing time. Similarly, in the transverse direction, the greater the deviation between the aspheric surface and the spherical surface (i.e., the asphericity), the "steeper" the surface, and the higher the processing cost.

Overview of Precision CNC Machining for Aspheric Surfaces​​

The material removal process generally consists of two steps:

First, a precision grinding wheel is used to mill the spherical blank into an aspheric contour that meets the required surface equation. This step must ensure minimal surface damage while initially achieving a certain level of form accuracy.

Second, polishing is performed. Pre-polishing completely removes the grinding-induced damage layer, followed by corrective polishing to repeatedly refine the surface until it fully meets the specifications for form accuracy and surface finish, as illustrated below:

Figure 2. Schematic diagram of CNC milling and polishing​​

Precision CNC Machining Process for Aspheric Surfaces​​

1. Spherical Surface Generating​​

The process begins by milling the best-fit spherical lens. This step, along with previous processes such as cutting and edging, follows the same procedures as traditional spherical lens manufacturing.

2. Milling/Grinding​​

This is a rigid material removal process. Precision grinding wheels are primarily categorized by shape into dish wheels and cup wheels.

​​Figure 3. Precision Grinding Wheels [1]​​

The milling process is divided into two steps: rough grinding and fine grinding:

Rough Grinding: Uses coarse-grit wheels (e.g., D64 grit) for bulk material removal, aiming to quickly shape the spherical blank into an aspheric contour. However, this stage leaves a relatively deep surface damage layer, which is not conducive to polishing.

Fine Grinding: Employs finer-grit wheels (e.g., D20 grit) to re-grind the surface, reducing the damage layer. If the form error is large (e.g., >3 μm), measurement data is incorporated to correct the shape to a higher precision (e.g., <3 μm).

Before milling, an appropriately sized grinding wheel must be selected based on the lens aperture. Parameters such as feed rate and rotational speed are optimized to achieve the best milling results.

3. Polishing​​

To describe the polishing process, Preston proposed the renowned Preston equation in 1927 [2]. Under specific conditions, the material removal amount ΔZ at a point on the surface within a given processing time can be expressed as:

Where:

​​K​​ is the Preston constant, determined by factors other than relative velocity and pressure;

​​ν​​ is the relative velocity between the polishing tool and the surface point (x, y) at time t;

​​P​​ denotes the polishing pressure.

According to this equation, when ν and P remain constant, the removal amount ΔZ is proportional to time t. This empirical formula provides a theoretical foundation for subsequent numerical simulations and machining experiments.

Similarly, the polishing process is generally divided into two stages:

​​Pre-polishing​​: Tools such as polishing bonnets (see Figure 4) are used to completely remove the grinding-induced damaged layer. Other common polishing tools include sponge polishing pads, wheel polishing tools, and fluid jet polishing.

Figure 4. Polishing Bonnets​​

If the surface figure does not meet the requirements, corrective polishing is performed. The specific process is as follows:

(1) Measure the surface figure error of the optical component to obtain the current surface figure data.

(2) Compare the data with the ideal surface figure, import the error into the equipment, and derive the material removal distribution function ΔZ for the current machining cycle.

(3) Set the polishing parameters, calculate the dwell time and optimized tool path. The computer then simulates the polishing result. If the outcome is unsatisfactory, the polishing parameters are reselected and the simulation is rerun.

(4) If the simulation result is feasible, initiate corrective polishing for one machining cycle.

(5) After the cycle is completed, measure the workpiece surface figure again. The data obtained is used as the input for the next corrective polishing cycle. This iterative process is repeated until the surface figure accuracy meets the specified requirements.

The control flowchart is shown below:

Figure 5. Aspheric Surface Polishing Process Flowchart​​

4. Inspection​​

Parameters such as surface finish and dimensions are inspected.

CNC machining equipment is expensive, and the process features low material removal rates and long cycle times. These factors are the primary reasons for the relatively high cost and limited production capacity of this technical route. This method is suitable for small to medium batch production of aspheric components requiring high surface figure accuracy and damage threshold, using materials ranging from DUV to IR.

Continuing to Advance the Frontiers of Aspheric Precision Machining​​

CASTECH utilizes advanced OptoTech ultra-precision CNC grinding and polishing equipment. Guided by measurement data from Taylor Hobson profilometers, CASTECH's engineers persistently push the limits of aspheric surface precision, achieving industry-leading performance across various machining indicators:

​​Table 1. Specifications for CASTECH's Aspheric Products​​

It is noteworthy that for specific client requirements demanding extremely high surface figure accuracy, we can currently achieve a PV/IRR precision of λ/10 (@633nm) through corrective polishing. 

Below are two case of CASTECH's capabilities in CNC precision machining of aspheric products.

Case 1: High-Precision "Super-Hemisphere"​

As mentioned previously, the "steeper" the aspheric surface, the greater the machining difficulty and the more challenging it is to correct the surface figure. In this case, a "super-hemisphere" with an outer diameter of φ=30mm (Clear Aperture=25.5mm), our team utilized a 2D corrective polishing method to achieve a final surface figure of IRR=0.191 µm. This approach significantly reduces costs compared to 3D polishing processes. This product has now entered batch production. The test report is shown in the figure below:

Figure 6. Test report for the φ=30 mm (CA=25.5 mm) "super-hemisphere" product​​

Case 2: Ultra-Large Aperture with Ultra-High Precision​​

For a parabolic lens with an outer diameter of φ=170 mm and a radius of curvature R=2000 mm, the achieved specifications within the clear aperture (CA=155 mm, central hole φ=20 mm) are a surface figure accuracy of PV/IRR ≈ 70 nm and RMSi = 13 nm. The test report is shown in Figure 7:

Figure 7. Test report for the parabolic lens with φ=170 mm, R=2000 mm​

Reference:

[1]https://www.optotech.de/files/downloads/products/catalogue_consumables_precision_optics_0.pdf

[2]Preston, F.W. (1927) The Theory and Design of Plate Glass Polishing Machines. Journal of the Society of Glass Technology, 11, 214-256.