Fabrication of an Infrared Shack–Hartmann Sensor by Combining High-Speed Single-Point Diamond Milling and Precision Compression Molding Processes

Abstract

A novel fabrication method by combining high-speed single-point diamond milling and precision compression molding processes for fabrication of discontinuous freeform microlens arrays was proposed. Compared with slow tool servo diamond broaching, high-speed single-point diamond milling was selected for its flexibility in fabrication of true 3D optical surfaces with discontinuous features. The advantage of single-point diamond milling was that the surface features can be constructed sequentially by spacing virtual spindle axes at arbitrary positions based on the combination of rotational and translational motions of both the high speed spindle and linear slides. By employing this method, each micro lenslet was regarded as a microstructure cell by moving the virtual spindle axis pass through the vertex of each cell. An optimization arithmetic based on minimum-area fabrication was introduced to the machining process to further increase machining efficiency. After the mold insert was machined, it was employed to replicate the microlens array onto chalcogenide glass. In the ensuing optical measurement, the self-built Shack-Hartmann wavefront sensor was proven to be accurate in infrared wavefront detection by both experiments and numerical simulation. The combined results showed that precision compression molding of chalcogenide glasses could be an economic and precision optical fabrication technology for high-volume production of infrared optics.

1. INTROCUTION

Since its invention in the early seventies, the Shack-Hartmann wavefront sensor (SHS) has been widely employed in a variety of applications and achieved great successes in ophthalmology and adaptive optics [1]. The SHS is a unique but important optical device used for wavefront detection and measurement. However, limited by available manufacturing technologies, many inventions based on SHS are focused on work in the visible band in the following areas: collimation [2], arithmetic [3,4], dynamic range [5,6], and precision manufacturing method [12–18]. The SHS working in the infrared range is less reported, especially for affordable SHS fabrication and measurement.

Most recently, chalcogenide glasses are used to fabricate infrared optical elements in thermal imaging devices, such as night-vision systems and thermal projectors [7]. These materials are made of chalcogen elements (S, Se, Te) instead of oxygen to bond with heavy metals and metalloids by covalent bonds [8]. The transparency can be observed up to 13.0 μm for sulfide glasses, 17.0 μm for selenide glasses, and 20.0 μm for telluride glasses [9]. In addition, chalcogenide glass can be precisely molded into the final shape in a single operation, by applying heat and pressure without significant changes to the internal structures in the finished optical elements. These optics provided optical industry with the material candidates for low-cost and high-performance devices.

Precision glass molding is being considered as an alternative to conventional methods for manufacturing high-quality and high-volume optical components [10]. In this process, compression molding of glass preforms is conducted at elevated temperature under highly controlled conditions, such as vacuum shield, constant temperature and loads. The final process temperature depends on the individual glass type. Chalcogenide glasses are ideal candidates for precision glass molding technology because of its low transition temperature (T_g) and steady physical & chemical property around T_g. For high-volume production, precision glass molding is preferred over more conventional methods, for increased efficiency because molding cycle is much shorter than the process of grinding, polishing or single-point diamond turning [11]. Production costs are also decreased because the molds can be reused for fabrication of thousands of replications without major wear or deformation.

As a key component in precision glass molding tool, the mold insert can be fabricated using several methods. The list includes but not limited to ultraviolet (UV) lithography [12–14], diamond turning [15], diamond micromilling [16], diamond flycutting [17], and electro-forming process [18]. However, some of these fabrication methods such as lithography process must be combined with other processes, e. g. plasma or wet etching. In comparison, ultraprecision diamond turning, milling and flycutting methods do not require other mechanical processes thus have more flexibility and high precision. Our previous work demonstrated that typical microlens arrays were fabricated by combining single-point diamond milling and injection molding [19]. There are minor deviations in geometry and surface roughness between the mold insert and the molded microlens arrays. Single-point diamond milling does have some drawbacks, for example, it has a relatively small bandwidth, due to the large inertia of the mechanical slides, therefore productivity maybe low.

Furthermore, with respect to some complex discontinuous geometries, several innovative diamond turning methods have been proposed. For instance, diamond micro chiseling and special Guilloche machining technique were proposed to generate retroreflective and microstructure arrays [20], respectively. However, these methods are not suitable to generate structures with variable shapes. Virtual spindle based tool servo diamond turning is another approach in discontinuous geometry manufacturing [21]. However, even equipped with a fast tool servo, the relatively small traveling range, typically much less than 1 mm [19], limited its manufacturing potentials. In this project, our option is high-speed single-point diamond milling to fabricate the microlens array mold insert.

In this research, an infrared plano-convex microlens array is designed and fabricated by combination of virtual spindle based single-point diamond milling and precision glass molding process. Aided by minimum-area tool-path generation arithmetic, the virtual spindle based single-point diamond milling provides a universal and effective solution to the fabrication of microlens arrays on the mold insert. Chalcogenide glasses, instead of traditional infrared materials such as Ge or ZnSe, are selected for producing high-precision infrared microlens arrays by glass molding. The geometries and surface roughness of the molded microlens arrays are measured and examined. Assembled with an IR detector, the optical property of the microlens array and the validity of the infrared SHS are demonstrated as well.

2. VIRTUAL SPINDLE BASED SINGLE-POIND DIAMOND MILLING

The basic idea of the virtual spindle based high-speed single-point diamond milling is to shift the rotational axis through the vertex of each single microlens virtually. The movement of the rotational axis is completed by combining the 2D translational motions of the machine servo control. Meanwhile, the motions along the axis directions are employed to generate complex microlens geometry. By shifting the virtual axis to the vertex of each lenslet, the large-area discontinuous microlens array can be fabricated sequentially, until the entire machining process is completed.

A. Kinematics of the Virtual Spindle based Single-point Diamond Milling

The kinematics of moving virtual spindle is illuminated in Fig. 1. The o_m-x_my_mz_m and o_t-x_ty_tz_t are the machine coordinates and working coordinates, respectively. At the initial stage, the machine coordinates are coincident with the working coordinate, as show in Fig. 1 (a). Meanwhile, the three directions of the local coordinates of lenslet o_s-x_sy_sz_s are set the same with the machine coordinates. During machining, the machine coordinates remain unchanged, while the working coordinates are being shifted from one local coordinate system to another one at a time, as shown in Fig. 1 (b) and 1 (c).

Fig. 1.

Schematic of kinematics of the virtual spindle based single-point diamond milling, (a) initialization of the diamond milling, (b) position and axis transfer, and (c) spiral milling.

In order to generate the geometry of each lenslet on the plane surface, the position of the working coordinates need to be changed from one place to another and each local machining process to be treated as an independent one. The details of this process can be summarized in the following steps.

Step 1, initialization

Like conventional diamond turning, the working coordinate system o_t-x_ty_tz_t is first moved to the center of the work chuck and aligned with the machine coordinate system o_m-x_my_mz_m. Each local coordinates o_s-x_sy_sz_s of a lenslet were virtually constructed with the same directions of the machine coordinates, as shown in Fig. 1 (a).

Step 2, position transfer

Transfer the working coordinate system o_t-x_ty_tz_t to the local coordinate system o_s-x_sy_sz_s by moving the 2D slides of the machine (Δx and Δy). Because the direction of these three coordinate systems are the same, the working coordinate and the local coordinate system are coincident, as shown in Fig. 1 (b).

Step 3, rotation around virtual axis.

In the local coordinate system, the o_sz_s was set as the rotational axis. To make the point o_s the fixed point on the o_s-x_sy_s plane, the rotational motion around the o_sz_s virtual axis was induced by the harmonic oscillations (Δx(t) and Δy(t)) with the same frequency on the x_s- and y_s-axis, as shown in Fig. 1 (c).

Step 4, local spiral diamond milling

Since the working coordinates and the local coordinates were coincident, similar to the conventional diamond milling process, the diamond milling tool is moved to the surface and the geometry of each lenslet is generated as an independent process. When the lenslet was finished, repeated the Step 2 and Step 3 for the next microlenslet milling until every lenslet is completed.

B. Toolpath Generation Arithmetic

In order to have a clear description and understanding of the machining process, further works on toolpath generation needs to be completed. The toolpath for the hexagonal microlens array layout is generated by MATLAB. The pitch and radius of curvature for each lenslet are 600 μm and 8.845 mm, respectively.

Based on the machining strategy for the microlens array stated above, the toolpath of the diamond tool in the machine coordinates o_m-x_my_mz_m is illustrated in Fig. 2 (a). As aforementioned, the toolpath for each lenslet in the microlens array can be treated as an independent machining process. After one lenslet was finished, the working coordinate system o_t-x_ty_tz_t is transferred to another position and aligned with the local coordinates of the lenslet. By shifting each local coordinates of the lenslet, the entire microlens array can be finished in sequence.

Fig. 2.

Schematic diagrams of (a) the virtual spindle based single-point diamond milling toolpath generation, and (b) optimization arithmetic by minimum-area fabrication.

To enhance machining efficiency of the milling process, the servo motion along the z_m direction was also optimized by following the principle of minimum fabrication area. As illustrated in Fig. 2 (b), similar to the conventional toolpath generation strategy, the toolpath for the diamond milling tool was divided into serval segments with constant cutting depth. However, each segment of the toolpath was different in length and coverage area. In this research, for example, in the first cycle, only the material in the central part was removed from the surface, which covered a very small area. The surface outside the cutting tool radius envelope remained untouched. After the 1^st cycle, the diamond milling tool began the 2^nd cycle with a larger coverage. Such process would continue until the entire surface of the lenslet was generated. Unlike the conventional toolpath generation strategy, the minimum-area strategy reduced the machining time by taking out unnecessary toolpath in surface area.

C. Tool Radius Compensation and Error Analysis

For the envelope of the milling tool, the compensation of tool radius was analyzed by using vector mathematics. Like the tool compensation in diamond turning [22], the normal vector n of a point on the freeform by using partial derivative of the surface equation. The normal vector can be expressed as follows,

$$\mathit{n}=\left(-f_x,-f_y,1\right)=(\cos \alpha ,\cos \beta ,\cos \gamma )$$ (1)

where f_x and f_y are partial derivatives with respect to x and y, and α, β, and γ are angels for directional cosines. For point p₀ (x₀,y₀,z₀) on the surface to be machined, the tool radius compensated point of the milling tool p₁ (x₁,y₁,z₁) in the n direction should be,

$$p_1=p_0+r\cdot \mathit{n}$$ (2)

The toolpath for single-point diamond milling is illustrated in Fig. 3 (a). In the milling process, the milling tool follows a spiral motion, same as diamond turning. Along the cutting direction, the motion of the diamond milling follows a straight line, no interpolation errors occurred in the machining process, as shown in Fig. 3 (b). While along the feeding direction, some residual marks remained on the machined surface, as shown in Fig. 3 (b). The amount of the surface principle error ranges between (min ε_f1 : max ε_fn).

Fig. 3.

Schematic diagrams of (a) geometry of the lenslet and tool radius compensation, and (b) errors in the cutting direction and feeding direction.

D. Finish Geometry Measurement

At the start, the mold insert was rough machined on a Haas VF-3 3-axis vertical machine center (Haas Automation, Inc., Oxnard, California, USA) from a 6061 aluminum alloy rod. For the final finished surface, an ultraprecision machine (Moore Nanotechnology, Inc., Keene, New Hampshire, USA) with five-axis servo motions was employed to generate the microlens array. The diamond milling tool (K&Y Diamond, Ltd., Diab St-Laurent, Quebec, Canada) has a 0.503 mm tool nose radius that was compensated in the generation of the spiral tool path trajectory. For all the molds used in this research, initial milling depth was 5–10 μm and finish milling depth was 2.0 μm at 40,000 rpm. The feedrates for rough and finish milling were set at 10 and 5 mm/min, respectively.

After machining, the optical surface profiler, white-light interferometer (Wyko NT9100, Brukner, Tucson, Arizona, USA) was employed to capture the microstructures of the machined surface, with 2D and 3D features. The microscope photograph of the machined surface is illustrated in Fig. 4 (a), which shows that the machined microlens array with good uniformity. The 2D surface profile further proved that the finished surface was smooth with really sharp line at the boundaries, as shown in Fig. 4 (b). Besides, the surface roughness of the lenslet was around 15.6 nm, adequate for requirements of infrared optics. Moreover, a 3D surface profile was presented in Fig. 4 (c) with an area of 3.0 × 3.2 mm² by stitching multiple sub scans. Finally, the cross-section profile on the A-B line was obtained from the 3D surface measurement.

Fig. 4.

Characteristics of the generated hexagonal microlens array, optical images with amplifications of (a) 2.5×, (b) 2D micro-topography, (c) 3D micro-topography, and (d) 2D profile along the cross-section A-B.

As illustrated in Fig. 4 (d), the 2D cross-section profile of the A-B line, the aperture of the machined lenslet is 605.2 μm. Compared with the design value 600 μm, the profile of the machined surface matched the initial design well. The depth of each lenslet is 5.503 μm, close to its theoretical value of 5.089 μm. The microscope photo also showed that the vertex of each machined lenslet was somewhat rough with poor contrast, which indicated that the quality of this local area was worse than the surface around it. This was mainly due to two reasons. One was the sampling frequency on the spiral curve near the vertex became lower than that on the spiral with large radius. Although the increment is reduced to half of the initial step size, the quality of the machined surface around vertex is still lower than the lenslet edges. The other reason may be that the tangential cutting speed became smaller when the milling tool approached to the vertex of the lenslet. Based on the tool radius compensation strategy stated in section 2.C, when the milling tool moved to the lenslet vertex, the contact point is gradually transferred to the rotational axis of the milling tool, leading to cutting speed decline. In order to minimize the influence of cutting speed variation to the surface quality, faster rotational speed (up to 60,000 rpm) was adopted to compensate the cutting speed loss. Fortunately the slight lack of quality near the vertex of the lenslet only introduced minor effects for infrared molds as shown in the following experiments.

3. COMPRESSION MOLDING PROCESS

After the mold inserts were fabricated, the compression molding process was employed to replicate the geometry on the molds to the infrared glass at molding temperature. The glass compression molding process was conducted on a commercial molding machine with Model# GP-10000HT (Dyna Technologies, Inc., Sanford, Florida, USA). A small piece of chalcogenide glass (As₂S₃) disk with both sides polished was placed between the upper and lower molds. After three cycles of purge with nitrogen, the temperature monitored by thermal couples reached 220 °C and the upper mold pressed onto the chalcogenide glass disk with 350 N load. To ensure the cavity was fully filled, the upper mold was continuously pushed downward until its position remained unchanged for ~5 min. Then the external fan was turned on and the temperature was reduced to ~40 °C. The molded microlens array was then demolded from the insert. The entire process is shown in Fig. 5.

Fig. 5.

Schematic diagrams of the compression molding process (I) preparation, (II) heating, (III) pressing, and (IV) cooling.

Further measurement was conducted to obtain the surface profile and quality after molding. As part of measurement tests in mold fabrication, the surface microscope photos, 2D, 3D, and cross-section profile were completed on the Wyko optical profiler. The microscope photos of the molded surface with large area presented the uniformity of microlens array, as shown in Fig 6 (a). A 2D and 3D local area with 2.7 × 3.0 mm² profile of the microlens array is shown in Fig. 6 (b) and 6 (c). Apart from the vertex of each lenslet, the molded surface of the microlens was as smooth as the mold surface with the sharp ridges at the boundaries. However, the vertex of each lenslet appears to be replicated with small pits, most likely due to the surface issues near the vertex of each lenslet on the mold left by the fabrication process which was discussed earlier. Finally, the cross-section of the molded geometry showed that the pitch was about 603.8 μm, which was close to the mold geometry 605.2 um. The measurement result showed that the geometry on the mold had been successfully transferred to the chalcogenide glass.

Fig. 6.

Characteristics of the molded infrared microlens array, optical images with amplifications of (a) 2.5 X, (b) 2D micro-topography, (c) 3D micro-topography, and (d) 2D profile along the cross-section A-B.

4. EXPERIMENTAL RESULTS AND DISCUSSION

SHS is a common optical device often used in adaptive optics systems, lens testing and increasingly in ophthalmology [23], which is employed to measure the wavefront in an optical system. If the microlens array, the critical component of the SHS assembly can be molded, it will provide an alternative for low cost optics with high fidelity.

A. Principle of Shack–Hartmann Wavefront sensor

The basic principle of wavefront measurement is by integrating several small lenslets to split the incident light into multiple apertures. As illustrated in Fig. 7 (a), the detection plane is placed on the focal plane of the micro lenslets. When a plane wavefront passes through the micro lenslets, each focal point will fall on the light axis, as the black line in Fig. 7 (a). However, when a distorted wavefront passes through the micro lenslet, the focal point will deviate from the central point. Since the deviation of the focal point was proportional to the slope of the wave plane, the slope angles g_xi and g_yi of the wave plane can be determined by [19],

$$g_{xi}=\frac{\mathrm{\Delta }x}{f}$$ (3)

$$g_{yi}=\frac{\mathrm{\Delta }y}{f}$$ (4)

where f is the focal length of the micro lenslet, and Δx and Δy are the displacement of the focal point from the central point of the hexagon. i is index.

Fig. 7.

Schematic diagrams of the optical principle of (a) single lenslet, and (b) microlens array for wavefront measurement.

Based on the measurements from the micro lenslets, the whole wavefront can be divided into small apertures, as shown in Fig. 7 (b). Combining the slope of sub-wave plane from each lenslet, the wavefront can be reconstructed by modal reconstruction method. If we use the Zernike polynomials to describe the reconstructed wavefront, the partial derivatives of Zernike polynomials are equal to the slopes on x and y directions from each lenslet [4], where i, m, and n are indices.

$$g_{xi}=\frac{1}{A_i}{\iint }_{A_i}{\sum }_{j=1}^n{a}_j\frac{\partial {\mathrm{Z}}_j(x,y)}{\partial x}dxdyi=1,2,3\dots ,\text{m}$$ (5)

$$g_{yi}=\frac{1}{A_i}{\iint }_{A_i}{\sum }_{j=1}^n{a}_j\frac{\partial {\mathrm{Z}}_j(x,y)}{\partial y}dxdyi=1,2,3\dots ,\text{m}$$ (6)

B. Optical Setup and Wavefront Measurement

To demonstrate the accuracy and precision of the infrared SHS constructed using a molded lens, a spherical wavefront measurement test was conducted. The core components of the infrared measurement system include an IR microlens array, an IR detector and an IR light source. The optical principle and experimental setup are illustrated in Fig. 8 (a). The microlens array was mounted on the camera at a distance from the focal plane equals to its focal length. A standard Germanium (Ge) plano-convex lens (Thorlabs Inc., Newton, NJ, USA) with anti-reflective (AR) film coated was mounted on a two-axis microstage. It was employed to generate a spherical wavefront with a focal length of 50 mm. The spherical wavefront passed through the microlenses and was focused on the infrared detector imaging plane. The infrared camera (Sofradir EC, Inc., Fairfield, NJ, USA) incorporated a 640 × 480 microbolometer detector (spectral range 8–14 microns) array, delivers high quality images in VGA format. The light source was a multiple wavelength coil-wound (ranging from 6.0 to 14.00 μm based on input power), supported IR source (HawkEye Technologies, Infrared Source IR-35, Milford, Connecticut, USA) mounted on a TO-5 header combined with a parabolic reflector to collimate the infrared light beam. The whole optical setup was shown in Fig. 8 (b). Some detailed parameters of the self-made SHS are listed in Table 1.

Fig. 8.

(a) Schematic of the optical setup, and (b) experiment setup.

Table I.

Parameters for the Infrared SHS

Property	Value
Pitch (μm)	600
Radius of curvature (mm)	8.845
Pixel size (μm)	17
Pixel array	640×480
Focal length (mm)	5
Number of spot	216

In the experiment, the distance between the spherical lens and the microlens array was set at 90 mm. Fig. 9 (a) and 9 (b) presented the reference image and the measurement image with 8.0 μm infrared light, respectively. In the photos from the infrared detector, the intensity of the surrounding noise is low when compared with the intensity of the focal spots of the lenslets. In order to reduce the influence of the surrounding noise to the accuracy of the measurement, several options are utilized. One is to setup a threshold for the image to filter out the light spots. After that, a small area near the center of the image was employed due to large contrast of light intensity. Then, multiple images were taken under the same conditions every ~0.5 s and the background noise was averaged out. The light spots that were used in the measurement were marked in Fig. 9 (c) and 9 (d).

Fig. 9.

(a) Reference image, (b) measurement image from the infrared detector and the acquired focal spots from (c) reference image, and (d) measurement image.

Based on the identified valid focal points on the reference image and measurement image, the deviations along x and y directions can be obtained for each focal point, as shown in Fig. 10 (a). Then the Zernike polynomials are used to reconstruct the wavefront. Fig. 10 (b) and 10 (c) presented the reconstructed and simulated wavefront profiles, respectively. The height of the wavefront is 0.2050 mm over the 8.085 mm pupil diameter in the measurement, and the estimated theoretical value is about 0.2048 mm. The deviation is 0.0012 mm or about 15% of the incident light (8.0 μm), indicating that the measured profile matches well with the numerically simulated profile, as shown in Fig. 10 (d). The main errors come from misalignment of the measurement system and imprecise displacement measurement between the spherical lens and the SHS. The measurement results demonstrated that the fabrication of infrared method used to create the microlens array was adequate for precision infrared optics manufacturing.

Fig. 10.

(a) Focal point displacements from their original positions, (b) reconstructed wavefront using SHS, (c) MATLAB simulated wavefront, and (d) errors between the measurement and simulation.

5. CONCLUSION

In summary, this research provides a new manufacturing method by combining high speed single-point diamond milling and precision compression molding for fabrication of infrared microlens arrays that can be used in SHS systems. In single-point diamond milling, the rotational axis with working coordinates o_t-x_ty_tz_t was transferred from each local coordinates o_s-x_sy_sz_s to the next location and rotated around the virtual axis by combining x and y harmonic oscillations motions. By using this configuration, fabrication of each lenslet can be treated as an independent process. The minimum-area fabrication strategy toolpath generation reduced the manufacturing time by removing the unnecessary toolpaths in the air. Further analysis was conducted to reduce manufacturing errors in diamond milling process. After the mold insert was fabricated, an infrared microlens array was molded and measured. At last, the molded microlens array was installed as part of the SHS with an IR source and an IR detector. Experiments showed that the SHS can perform accurate wavefront measurements. The same manufacturing strategy, combining high speed single point diamond milling and precision compression molding, can be applied to fabrication of many other micro- and nano-scale optics to improve production efficiency and product quality.