Representaciones sociales La segunda categoría es representaciones

In scientific terms, a wavefront may be defined as “the surface over which an optical disturbance has constant phase” or “the surface which joins individual points on rays which have the same optical path length”. The optical path length is simply the distance a ray travels, multiplied by the refractive index of the material travels in. For an ideal plano lens, the exiting wavefront surface should be a plane which means the exiting wavefront error should be zero. However, injection molding process can introduce inhomogeneous index distribution across the part. If the part geometry is perfectly flat on both side and two sides are parallel to each other, the index change in the lens can be obtained from the measurement of wavefront change.

In reality, lenses with perfect geometry are hard to come by for index measurement thus we need to remove the effect of geometry error. One solution for the surface geometry compensation is to submerge the molded lenses into an index matching fluid, a special fluid with nominal refractive index that matches that of PMMA. The index variation can be measured by a wavefront measuring system, such as a Shack Hartmann sensor (SHS). SHS has been widely used in both precision optical and vision science research with object to sample various points on the emerging wave and derive the shape of the wavefront. In essence, a Shack-Hartmann plate is a series of microlenses arranged in a linear fashion. Each lenslet focuses a view of the point source through

displacement and the focal length of the lenslet as shown in Figure 4.7 [Trusit, 2004]. After examining the slope at each micro lenslet in the x and y meridian, the entire wavefront can be plotted in 3D format. The wavefront error which describes the optical path difference between the measured wavefront and the reference wavefront is derived mathematically from the reconstructed wavefront.

Figure 4.7: Calculation of the slope of the wavefront at individual lenslet

A typical SHS based measurement setup is shown in Figure 4.8. The filter in the optical path is used to adjust the intensity of the laser to avoid saturation on the sensor. The aperture of the Hartmann sensor is 6.4 mm × 4.8 mm of a rectangular shape. If large size samples are measured, beam reducer is needed in the measurement setup.

∆y

θ

θ

Optical axis of lenslet Measured wavefront

Plane wavefront Position of laser spot for

measured wavefront Position of laser spot for calibrated plane wavefront

Single micro lenslet CCD device

Because of different slope, each section of the wavefront will be imaged at different position on the CCD (Coupled Charge Device) in the SHS system. The system error will be nullified prior to taking each measurement. With the aid of the matching fluid, index variations can be mapped for the entire molded lens. The different index variation for the lenses molded under different process conditions can be transferred into geometry changes in the optical system. This information is useful for mold compensation.

Figure 4.8: Index measurement setup

The measurement results are shown as follows. The unit for the color bar is Microlens Array CCD camera Hartmann Sensor Beam Reducer Test lens Matching Fluid He-Ne Laser Filter

In Figure 4.9 (a), the mold temperature was 150 °F while in Figure 4.9 (b), it was 190 °F. In this experiment, only mold temperature was adjusted, all other process parameters were kept unchanged. The flow direction is from left to right. From the measurement results, it can be seen that higher mold temperature will bring smaller index deviation distribution.

(a) Lower mold temperature (b) Higher mold temperature

Figure 4.9: Wavefront error of the molded lens under different mold temperature in fluid

In Figure 4.10 (a), the packing pressure was 35 % and 27 % in Figure 4.10 (b). In this experiment, only the packing pressure was adjusted, all other process parameters were kept the same. From the measurement results, it can be seen that lower packing pressure will also introduce smaller index variation in the lens.

(a) Higher packing pressure (b) Lower packing pressure

Figure 4.10: Wavefront error of the molded lens under different packing pressure in fluid

With the aid of the optical matching fluid, we can determine the average index distribution in the part. While for the real optical system, the optical elements cannot be immersed into the matching fluid. When the lens is used in the air or other media, the wavefront aberration from the part is not only caused by inhomogeneous index but also by geometry error. Sometimes the geometry error may compensate for some index change in the part, so the RMS (root mean square) value for the wavefront may actually be smaller than that in the matching fluid.

The same lenses as in Figure 4.10 (a) and (b) were also measured in the air. The measurement results are shown in Figure 4.11.

much better than that of the lens molded using 27% packing pressure, so the measurement result in the air does make sense. In this case, the surface geometry of the lens in the lower packing pressure brings more aberration to the wavefront error.

(a) Higher packing pressure (b) Lower packing pressure

Figure 4.11: Wavefront error of the molded lens under different packing pressure in air

The index deviation measurements can be used for mold compensation. Combining the surface and thickness measurement results and index distribution, the modified mold inserts can be designed and fabricated. With the modified freeform mold, the molded lens will bring improved optical performance.