Binary Diﬀraction Grating Design - Photonics Element: Diﬀraction Grating

6.3 Photonics Element: Diﬀraction Grating

6.3.1 Binary Diﬀraction Grating Design

A binary grating with a period (pd) of 265μm, height (h) of 75μm, and ridge width (c) of 95 μm was designed using the Fourier Modal Method [120–

122]. To excite a guided-mode resonance, we assumed a titanium dioxide (TiO2) coating of thickness 38μm. Figure 6.9 shows the cross-sectional design structure of the grating. The reﬂectance of the structure over a wavelength

Figure 6.9: Binary grating design for THz application.

region from 0.3 mm to 0.5 mm is shown in Figure 6.10. The optimized

Figure 6.10: Reﬂectance of the binary grating in the millimeter wavelength region.

grating exhibits a peak reﬂectance of 82.62% at λ = 385.5 μm, and the full width half maximum of the resonance peak is 50.2μm.

6.3.2 3D-printed Diﬀraction Grating

The binary grating design in CAD format without the TiO2coating is shown with the 3D-printed binary grating in Fig. 6.11(a and b), respectively.

! "

#$%&'

Figure 6.11:Diffraction grating for realizing a guided-mode resonance ﬁl-ter: (a) CAD design layout of a binary grating design and (b) the 3D-printed gratings. Top view of the surface proﬁle of the binary grating printed on (c) the glass substrate and (d) printed plate. (e) Cross-sectional view of the grating through SEM imaging.

Scanning Electron Microscopy is used to measure the surface proﬁle of the printed binary grating after sputter coating it with silver [123]. The lat-eral surface proﬁle of the printed grating, as shown in Fig. 6.11(c), is de-pendent on the substrate onto which the droplets from the ink-jet printer are deposited. This effect is removed after using a printed substrate plate, see Fig. 6.11(d). The height variation of the periodic structure is observed from the side cross-section of the printed grating as shown in Fig. 6.11(e).

Even though the period and height proﬁle of the grating are different from the design, the results show a promising way of 3D-printing grating struc-tures (especially sinusoidal gratings) by optimizing the printing process of Printoptical^c Technology. Thus, the experimental measurement of the grat-ing reﬂectance can be done in the future after optimizgrat-ing the printed struc-ture and coating it with TiO2.

6.4 PHOTONICS ELEMENT: DIFFUSER

Multifaceted diffusers that can help to generate partially coherent pulse trains out of fully coherent pulse trains are designed and printed as shown in Fig. 6.12. The diffuser is rotated in such a way that each individual pulse in the incident pulse train passes through a different facet of the diffuser.

Each facet then introduces a different spectral phase that leads to an indi-vidual pulse shift in time, thus making the pulse train partially coherent by introducing jitter [8, 124, 125]. The designed diffuser, shown in Fig. 6.12(a), has 38 sections with a height variation in micrometer scale. The printed dif-fuser with a rough surface is shown in Fig. 6.12(b), where each section can be seen. In this case, the height proﬁles are assumed to have a uniform statisti-cal distribution. However, the height proﬁles can also have, e.g., a Gaussian

Figure 6.12:Experimental setup using 3D-printed Diffuser.

statistical distribution.

The theoretical background related to creating temporally partially co-herent pulse trains using the printed diffuser is presented in more detail in Ref. [8]. The experimental measurement setup is based on a Mach-Zehnder interferometric technique, and the results demonstrate the capability of the diffuser to convert a temporally fully coherent pulse into a partially coherent pulse train.

6.5 DISCUSSION

In general Printoptical^c Technology can be applied to 3D-print various op-tical/photonics components. The quality of the 3D-printed elements can be determined by characterizing the surface proﬁle deviation. However, char-acterizing the surface of the printed elements can be tricky based on the complexity of the surface. For example, the metrology techniques that are applied for the centimetre-scale illumination optics are industrial standard surface characterization methods. In contrast, surface characterization of imaging optics has to be accurate in optical wavelength range. Thus, char-acterization of the 3D-printed aspherical lens could not be performed using the proposed Mach–Zehnder testing setup due to its limitation to spherical wavefronts. Further improvement on the setup using an automated surface positioning [126] could provide a way to characterize an imaging quality 3D-printed asphere or freeform lenses.

7 EXPERIMENTAL OPTICAL PERFORMANCE ANALYSIS

The performance of the printed optical components is demonstrated by con-structing experimental setups and by measuring the target irradiance distri-butions, including image sharpness. The following sections show the mea-sured results of the printed optics for various applications.

7.1 FREEFORM LENSES

We begin with experimental characterization of the freeform optical elements introduced in Sect. 2, considering in particular the two case studies.

7.1.1 Case Study 1

The optical performance of the printed lens for uniform rectangular distri-bution was characterized using a White LED HSMW-A400-U00M2. The ex-periment was performed by placing the LED light source in front of the optics and by capturing the image of the obtained irradiance distribution with a camera, as shown in Fig. 7.1(a). The experiment show that the printed freeform lens direct the light into a rectangular form as shown in Fig. 7.1(b).

Even if the measured uniformity of the distribution looks qualitatively good overall, the magniﬁed images shown in Fig. 7.1(c) demonstrate the parallel continuous blurred lines on the target distribution which is due to the print-ing process that is sometimes also visible on the optics as lines. This issue has been found to be manageable for lens with less trajectory on external surface. However when the thickness of the freeform lens is in cm-scale and has high steep angle, the printing process could only be optimized for ei-ther achieving high optical performance with less scattering like in this case uniformity, or directing the light accurately into the required form.

Figure 7.1: Irradiance distribution for uniform rectangular illumination case study: (a) schematic of the experimental measurement setup and (b) the experimentally measured target distribution. (c) The effect of printing error on the experimental target uniformity.

The experimental design layout and its practical implementation with printed lenses for paper web illumination case study is shown in Fig. 7.2 (a and b).

The aim was to improve the camera-system illumination of the paper web to detect issues like defects over the web width and cracks and wrinkles at the edges by using customized lens with low cost. To test the printed optics optical performance qualitatively, an electronic LED-module device with an integrated freeform lens array was constructed, as shown in Fig. 7.2(c). The experimental result in Fig. 7.2(d) demonstrates that the light distribution re-sembles the required 45^◦×35^◦ target illumination.

Figure 7.2: Design layout: (a) 3D-printed freeform layout of paper web illumination and (b) actual illumination of the paper web with an LED-based printed freeform lens array. (c) Illumination device using a 3D-printed lens array and (d) the experimental illumination distribution.

The optical performance of the printed lens for discontinuous beam shap-ing was characterized usshap-ing a white LED Lumex VAOL-S8YP4 LED at λ = 589 nm. The Lumex LED intensity distribution is close to the ideal Lam-bertian intensity distribution with normalized cross correlation coefﬁcient (NCC) of 99.2% [1]. The setup presented in Fig. 7.1 (a) is also applied for this case.

Figure 7.3 presents the results for the LED light splitter case study. The ex-perimental target distribution resembles the theoretical simulation. The dis-tortions shown in the target distribution of the printed lens could be caused by the surface proﬁle deviations or the inhomogeneity of the lens induced during the printing process.

Similarly, Fig. 7.4 shows the simulated and measured target irradiance distributions for the MTF-like case study. The results demonstrate that the experimental and simulated target irradiance distributions are quite close.

It can be seen from the ﬁgures that the widest ﬁve bright lines are clearly

Figure 7.3: Irradiance distributions for LED rectangular light splitter case study: (a) simulated and (b) experimental target irradiance distribution re-sults in comparison to the design designated area as shown with rectangle lines.

visible but the narrower lines are merged and difﬁcult to distinguish. This is due to the less steep slope change at the right part of the lens surface, and thus the effect of the ﬁnite extent of the light source causes the merging effect since the design was based on point source assumption.

Figure 7.4: Irradiance distributions for MTF-like case study: (a) simulated and (b) experimental target irradiance distributions.

-100 -50 0 50 100 Dimension [mm]

0 0.2 0.4 0.6 0.8 1

Average Relative Intensity (a.u)

Simulation using LED Simulation using point source Measurement using LED

Figure 7.5: Comparison of the average relative intensity of the MTF-like target irradiance distribution.

Figure 7.5 presents the average amplitude of the target distributions in y-direction. The demonstrated result shows that the MTF contrast decreases at the narrower lines even in the case of simulation using a point source (green line). This could be attributed to the resolution of the geometry, which is not sufﬁcient to resolve the contrast perfectly. The surface proﬁle deviation of the printed lens from the design is the major reason for the curve deformation in the measurement.

7.1.2 Case Study 2

The optical performance of the printed lens for case study 2 is far from the required target image as shown in Fig. 7.6(a) of the simulation result. This is due to the high surface proﬁle deviation of the printed lens relative to the design. However, if the surface proﬁle deviation could be decreased by a factor of 10, the target image of Lena would be observed as shown in Fig. 7.6(b). Such an order-of-magnitude improvement can be foreseen by further development of real-time monitoring of the printing process and by employing the iterative printing approach already used in this work for fabrication of imaging-quality lenses.

Figure 7.6: Simulated performance of the 3D-printed freeform lens for case study 2: (a) simulation of the actual printed lens. (b) The expected performance increment when the surface proﬁle deviation is decreased by a factor of 10.

7.2 FRESNEL AND CONVENTIONAL LENSES

The performance characterization of the Fresnel and spherical imaging lenses was performed using a goniometer and by building microscope setup, re-spectively.

7.2.1 Non-imaging optics: Fresnel lens

The optical performance of the printed Fresnel lens is characterized using metal girder for holding the printed unities and luminaire housing as shown in Fig. 7.7. Electrical tape was applied to remove light leaks between the printed lenses in the array as shown in Fig. 7.7(a). A goniometric setup in Fig. 7.7(c) was used to measure the obtained illumination, with the result shown in Fig. 7.7(d).

The measured light distribution looks qualitatively similar to the simula-tion, as evidenced in Figs. 7.8(a) and (b). The difference that is visible could be attributed to misalignment between the printed freeform lens matrices.

The heat from the LEDs bend the printed lens without returning to the orig-inal shape. The effect of LED intensity on the target distribution can be seen in Fig. 7.8(c), in which only 80% of the LED intensity has been achieved.

This result shows further work needs to be done on ﬁnding an alternative printing material that will endure the high-intensity LEDs.

Figure 7.7: Experimental setup for testing the Fresnel lens array: (a) 3D-printed Fresnel lens array placed in a lighting box and (b) the Fresnel lens array with LEDs. (c) Layout of the goniometer and (d) the measured target distribution.

Figure 7.8: Target distribution for the Fresnel lens arrays. (a) simulation, (b) printed (full intensity) and (c) printed (80% intensity).

7.2.2 Imaging Optics: Spherical Lens

The 3D printed spherical lens was characterized by constructing a micro-scope setup illustrated in Fig. 7.9 and resolving a USAF 1951-IX MTF (Ed-mund Optics) resolution test target. Then, the imaging resolution of the 3D-printed lens in contrast to the Thorlab LA1509 N-BK7 lens was measured using the Modulation Transfer Function (MTF) in reﬂection mode. The

chro-Camera Detector

Light collimating tube Aperture 3D printed objective lens

USAF 1951-1X Resolution tarrget Light Source

Spectral filter

Figure 7.9: Experimental setup of a microscope in reﬂection mode to char-acterize the 3D-printed lens image resolution.

matic aberration of the spherical (singlet) lenses was eliminated using a spec-tral ﬁlter centered at 550 nm and having a 100 nm passband.

Figure 7.10 demonstrates the imaging resolution of the printed and com-mercial N-BK7 singlet lenses. Considering the image resolving power of the human-eye, we used 10% MTF as a threshold. Thus, considering Fig. 7.10(c), the two elements of Group 7 corresponding to 143.7 lines/mm of the USAF resolution target are resolved by the 3D-printed lens. However, element 3 of group 7, which corresponds to 161.3 lines/mm, is resolved clearly by the commercial lens. The lower resolution of the 3D-printed lens could be due to the surface proﬁle deviations and/or the non-uniformity of the material inside the printed lens as compared to the commercial glass lens.

In comparison, Trioptics ImageMaster HR imaging quality testing de-vice [105], see Sec. 4.5, was applied to check the optical performance of the 3D-printed lens. The experimentally measured MTF values shown in Fig. 7.11 demonstrate that the MTF curve for the 3D printed and reference lenses are close to each other but below the diffraction limit. Zernike polyno-mial is used in Zemax Optic Studio 16 to aproximate the surface irregularity shown in Fig. 6.6 on the spherical lens design [127]. The imaging resolutions are recorded to be 125 lp mm⁻¹ and 135 lp mm⁻¹ at the 10% MTF thresh-54

Figure 7.10: Experimental imaging resolution comparison between the 3D printed and commercial singlet lenses. Record of the USAF 1951-1X MTF resolution target image for (a) the 3D-printed lens and (b) a commer-cial NBK-7 singlet lens with an aperture diameter of 12 mm using a green bandpass ﬁlter centered at 550 nm. Group 6-7 resolution target for the (c) 3D-printed and (d) commercial lenses. Magniﬁed images of Group 7 in (e) and (g), and cross-sectional intensity proﬁles in (f). The red line marks the results with the printed lens and light blue with the reference lens.

old, respectively, which are comparable to the results found using the USAF 1951 resolution target. The common limitations of polymer optics, such as scratch, could be the reason for the difference in the MTF curves. The

mea-sured focal length of the printed lens is within±3% tolerance value from the target, relative to ±1% for the commercial lens. This result demonstrates an advancement in optical performance to the ﬁrst batch of 3D printed lenses by Luxexcel [128].

0 20 40 60 80 100 120 140 160 180 200

Spatial Frequency [lp/mm]

0 0.1 0.2 0.4 0.6 0.8 1

Modulus of OTF

Measured result for Thorlab LA1509 N-BK7 lens Simulation result for ideal Thorlab LA1509 N-BK7 lens Diffraction limit for Thorlab LA1509 N-BK7 lens Measured result for LUX-Opticlear 3D-printed lens Simulation result for ideal LUX-Opticlear 3D-printed lens Diffraction limit for LUX-Opticlear 3D-printed lens Simulation result for LUX-Opticlear 3D printed lens considering surface profile deviation

Figure 7.11:MTF measurement results with ImageMaster (HR)

The 3D-printed lens can be used on various low-cost application areas like dermascope [42], ﬁeld imaging [129], and even as a microscope objective lens for resolving subpixels of LCDs, as demonstrated in Fig. 7.12. Other appli-cation areas of 3D printed lens could be found in low-cost Digital single-lens reﬂex (DSLR) mini cameras as shown in Fig. 7.13. The qualitative imaging results of the singlet lens show that the printed lens works relatively well, bearing in mind it is a simple plano-spherical lens.

The 3D-printed plano-convex lenses can be combined with diffractive structures using other patterning or fabrication techniques in order to im-prove the performance of the lens or to introduce new functionalities [130].

Thus, the technique presented here can be used as a starting step for 3D printing centimeter scale lenses for various applications such as full-functional eyepiece, which has been attempted in our group [131].

Figure 7.12: Resolution of LCD display pixels using the 3D-printed lens:

(a) LCD display and (b) resolved sub-pixels using the printed lens.

Figure 7.13: DSLR camera using 3D-printed lens : (a) the printed lens on the DSLR camera using mount and (b) arbitrary image taken through it.

7.3 DISCUSSION

The surface quality of the printed freeform lenses, especially the surface ﬁg-ure deformation, is the main reason for the deviations of the experimental results from the theoretical simulations. The material inhomogeneity of the printed lens that arises due to the printing process introduces a scattering effect, which leads to degradation on the optical performance like the uni-formity of the target distribution. To minimize this issue, we optimize the printing process. However, the size of the LED light source, fabrication error, and misalignment while characterizing the printed lens are the major con-tributor for the required target irradiance shape deformation. However, the surface measurement techniques for cm-scale freeform lenses are limited in accuracy and capability; for example, a steep surface cannot be measured using a Mitutoyo Formtrace contour measuring system. Thus, the measure-ment has been done only at the center of the printed lens using this device

for a relatively smooth surface withinμm scale accuracy. This becomes a bot-tleneck for doing an extensive analysis of the fabrication error; future work can be done in this area. On the other hand by using wavefront surface-error correction techniques, the surface proﬁle deviation of the printed spherical lens for imaging case has been decreased dramatically, permitting the manu-facturing of imaging-quality optics. At present, the technique only works for spherical wavefronts, but it can be upgraded in order to be used for freeform lenses by employing reference wavefronts generated with the aid of diffrac-tive/refractive hybrid elements.

In general, increasing the optical quality will lead to better optical per-formance. This can be achieved using new high-index printing materials, live surface error correction techniques, and by optimizing the printing pro-cess for individual cases. The shape of the printed lenses can be formed accurately by using thin layers (< 4.1 μm), since the lens is formed using staircase-based approximation of the spherical geometry. Such thin layers can be attained by using a smaller droplet size, < 17 μm in diameter. The small size of the droplets can also become useful in the error-correction it-eration stage. While placing each droplet at the exact location can become challenging, it could be manageable by learning the droplet location within the printing stage. This, however, might also increase the printing time.

8 SUMMARY AND OUTLOOK

In this thesis, designing optical elements such as free-form lenses using a source-to-target ray-mapping algorithm, as well as prototyping or small se-ries production of the designed elements using a 3D-printing technology called Printoptical^c Technology has been proposed and demonstrated. As an example, freeform lenses are designed for shaping a LED source dis-tribution into a uniform rectangular target disdis-tribution and complex target images. The performance of the proposed algorithm is comparable to other designing methods found in semi-commercial software, with an advantage of being customizable for various tasks. In addition, the numerical analy-sis of manufacturing defects on the performance of the designed freeform lenses have been investigated, and the results illustrate the sensitivity of the complex target illumination on submicrometer surface ﬁgure deformity of freeform lenses. Even if the freeform lens designing methods are sufﬁcient for the proposed 3D-printing manufacturing technology, further work can be done on the designing method like by expanding the custom algorithm into designing two freeform surfaces simultaneously for illumination application using an extended source.

Prototyping of centimeter-scale optics using the 3D-printing fabrication technique to reduce the manufacturing cost, time, and material waste has also been proposed and demonstrated. Printoptical^c Technology has been applied to print the optics by optimizing the printing process speciﬁc to each

In document Designing and 3D-printing optical components for imaging, illumination and photonics applications : a case study based on printoptical technology (sivua 59-0)