In past decade, diffractive optical elements (DOEs) [1–3] have been widely applied in various technology fields, including compact augmented reality display, modern optical security technologies, biomedicine and others, due to their small dimensions, low weight and flexible design.

Many methods have been developed to fabricate these DOEs. Photolithography [4] is one of the more common techniques. Although this method is able to mass produce pattern by using an optical mask, it is still difficult to manufacture various patterns and align the mask. Compared to photolithography, maskless lithography [5, 6] shows some undeniable advantages, such as low manufacturing cost, and the ability to fabricate in a large area. Among them, direct laser lithography uses a thermal technique to form a writing pattern that is a good candidate [7–10]. Because it is a maskless technique, it has the ability to change arbitrary lithographic patterns from one run to the next.

The elliptical zone plate (EZP) array [11], which keeps the circular zone plate shape in an off-axis optical system, was developed from a Fresnel zone plate array [12, 13]. This kind of zone plate array is used to reflect waves in micro optical platforms for all-optical demutiplexing [14] and to focus the light source into an array of spots in an off-axis system. Furthermore, the EZP array has been applied in organic light-emitting diodes (OLEDs) [15] and liquid-crystal displays (LCDs) [16]. However, it limits the light outcoupling efficiency in OLEDs and the brightness in LCDs because there is still some gap area which cannot contribute, thus reducing the total internal reflection between the adjacent microlenses [17].

The fill factor, which is defined as the percentage of the microlens area with respect to the total area, is one of the conditions used to determine the overall optical performance of a lens array [18, 19]. In our previous work, an EZP array was arranged in a rectangular layout with a low fill factor of 76% which leads to light loss [20]. A high fill factor EZP array, which was almost used in off-axis optical system, is in high demanded to enhance the light outcoupling efficiency in OLEDs and the image brightness in LCDs [21–24].

The original idea for high fill factor zone plate proposed by Niu et al. [23] was only used for on-axis optical systems. In Niu’s work, however, there was no clear experiment results and theory to compare image properties between two designs of Fresnel zone plate.

In this paper, a close-packed hexagonal EZP array with high fill factor used in off-axis imaging processing is proposed and fabricated by direct laser lithography. Experiment setups for focusing and imaging properties were introduced to evaluate and compare the optical performance of the high fill factor EZP array and the previous model.

A schematic diagram of the direct laser lithographic system for a rectangular type is shown in Fig. 1. An SLOC’s laser generated a lithographic source with a wavelength of 488 nm, which was focused onto the surface of the specimen by a Mitutoyo’s 100× objective lens with a numerical aperture of 0.7. To fabricate various patterns, a 2D (X- and Y-directional) air-bearing precision positioning stage was used to hold the specimen. To adjust the intensity and exposure time of the focused beam, we respectively used a commercial laser power controller (LPC) and a Thorlabs’ SC10 shutter. The LPC stabilized the lithographic source at a level of 0.03%. A computer used data acquisition (DAQ) to control LPC, shutter and stage through a general purpose interface bus (GPIB), transistor-transistor-logic (TTL) and recommended standard-232 (RS-232), respectively.

Figure 1. Configuration of direct laser lithographic system.

An EZP was developed consisting of a series of elliptical zones that were defined by

In Eq. (1), f is the focal length of the EZP; λ is the wavelength of the illumination laser beam; θ is the off-axis illumination angle; n is nth zone of the zone plate, and a_n and a_n/cos θ are the semi-minor and semi-major axes of the nth zone of the EZP.

To optimize the fill factor of the array, we modified the outside border of the classical EZP element and then arranged array layout, as shown in Fig. 2. Firstly, certain portions of the EZP were trimmed off to create a hexagonal border. This means that the (n – 1)^th zone of the EZP was inscribed in the hexagonal line. Secondly, we arranged the EZP elements in a hexagonal layout to decrease the gaps area between them. The distance between two adjacent focal points, which were received on a plan normalized to reflected beams, were of equal length. Therefore, the size of the hexagonal elliptical zone plates slightly descended, row by row.

Figure 2. Scheme of a high fill factor EZP array design.

To fabricate the high fill-factor EZP array, direct laser lithography using a thermal chemical technique [25] was employed, as shown in Fig. 3. In this method, after passing through an objective lens, the lithographic source was directly focused onto a chromium layer in a specimen creating Cr₂O₃ on its surface. This specimen was kept on the XY linear stage; therefore, the shape of the pattern depended on the moving path of this stage. To form a fine elliptical zone plate with an outside hexagonal border, the stage was moved in a zigzag motion. After completing the writing step, the target specimen was immersed in an etchant consisting of two solutions K₃Fe(CN)₆ and NaOH for three minutes. In this etching process, the Cr₂O₃ remained on the glass substrate while the bare chromium part disappeared and then, a final diffractive optical element was created.

Figure 3. Diagram of a trimmed elliptical zone plate fabrication using the thermal chemical technique.

The newly designed EZP array with high fill factor was fabricated by using the process above with a writing speed of 0.1 mm/s and a laser intensity of 10 mW, depicted in Fig. 4. The distance from center to center of the between two adjacent zone plates was 780 µm in the X-direction. For this high fill-factor design, an illumination light was incident on the surface of array at an angle of 45°, and the focal length from the first row of the array to the observation plane was 40 mm.

Figure 4. Measurement of a high fill factor EZP array.

To easily evaluate the advantages and disadvantages of the high fill-factor elliptical zone plate array, we also fabricated an array included EZP elements with classical shape but arranged in a close-packed rectangular layout with low fill factor. Its parameters are the same as for our proposed EZP array, a distance of 780 µm in the X-direction between the two centers of the adjacent zone plates, a focal length of 40 mm from the first row of the array and an off-axis illumination angle of 45°, as shown in Fig. 5.

Figure 5. Measurement of the previous EZP array model.

The optical properties of two elliptical zone plate array model were assessed by focusing on performance and imaging performance.

There was a fixed part which was used for both types of optical evaluation. It consisted of a Thorlab’s adjustable angle plate with a full 180° of movement to hold the DOE specimen, a Basler acA4112-20um complementary metal–oxide–semiconductor (CMOS) camera with a resolution of 4096 × 3000 pixels placed at the focal plane with distance of 40 mm from the designed DOE specimen to receive the beam coming from the specimen. The pixel size of the CMOS camera is about 3.45 µm × 3.45 µm, and a display connected to the CMOS to clearly observe the diffraction image.

To characterize the focusing ability of the two array models, a He-Ne laser with a wavelength of 632.8 nm and beam of diameter 1.5 mm was used as an illumination beam, as illustrated in Fig. 6(a). Because the size of this laser beam was small compared to the size of the array, this source was expanded using a beam expander before going to the target DOE. The observed focal spots of high fill-factor design and the old elliptical zone plate array design are shown in Figs. 6(b) and (c), respectively. The focal spots were distributed at the same distance of 780 µm, and their full width half maximum (FWHM) was 30 µm under the off-axis illumination angle of 45° for the two kinds of array. This demonstrates that the focusing ability of a high fill-factor elliptical zone plate was almost the same as the previous elliptical zone plate array. In addition, the crosstalk effect that appeared among elliptical zone plates in both model of arrays were not much different in average level as compared with each other.

Figure 6. Focusing performances of the proposed and the previous zone plate array. (a) Diagram of the focusing property evaluation of the arrays and diffraction images of (b) proposed EZP array and (c) previous EZP array.

To further investigate the imaging ability of this high fill-factor model, the illumination source was changed from the He-Ne laser to a flashlight. Four letters “NNHA” were placed close to the light source and in the front of the DOE with a distance of about 400 mm. In this case, it was not necessary to use a beam expander. After the light from the flashlight passed through the letters, it illuminated the specimen and then, the CMOS camera confirmed the diffraction image shown in Fig. 7(a). The letter images of two model EZP array were represented in Figs. 7(b) and (c) that had the same size of 13.083 × 13.083 inches and resolution of 96 pixels per inch. Compared to on-axis optical systems, elliptical zone plate arrays were used for off-axis optical systems that created the off-axis imaging aberrations that would cause distortion in these diffraction images. However, an elliptical zone plate provides two advantages for increase of image quality. First, the residual beam and the main source are not focused in the same direction and second, the light from the observation plane is not reflected back towards the beam source.

Figure 7. Imaging performances of the proposed and the previous zone plate array. (a) Diagram of the imaging property evaluation of the arrays and diffraction images of (b) proposed EZP array and (c) previous EZP array.

To compare the brightness between two letter images, we used a right hand side of luminance formula which is a weighted combination of the RGB components [26]

This standard algorithm is used by image processing software and designed to match human brightness perception. It was implemented by MATLAB and the results were given as 39.04 and 22.38 for the new EZP array and the previous model, respectively. In addition, the difference between maximum and minimum pixel intensity in Fig. 7(b) is more than in Fig. 7(c). Therefore, the diffraction image received from the high fill factor EZP array is brighter and clearer than the prior EZP array.

For a further theory demonstration, Wei et al. [27] reported that the luminance has a linear dependence on the area ratio of the microlenses, and is expressed as

The luminance perpendicular to the display without the microlens array pattern is B₀ when the target specimen is illuminated by a light source; B_microlenses is the luminance with the microlens array pattern; R_area is the area ratio; k₁, k₂ are numbers; A_microlenses is the area surface of the microlenses; A₀ is the total area of the device and A_gap is the area of gaps among the microlenses.

When the area ratio approaches to 1, the luminance is higher. In theory, brightness is the term for a subjective impression of the objective luminance measurement standard. In our case, luminance is used to characterize the brightness of diffraction images. This is the reason that the diffraction image of the high fill factor EZP array (R_area = 0.975) has more brightness than the close-packed rectangular EZP array (R_area = 0.76).

In this study, by optimizing the calculation design, a high fill-factor elliptical zone plate array was demonstrated. The direct laser lithographic system including an XY linear stage, which has the advantage of flexible movement such as zigzag motion, was used to fabricate the high fill-factor EZP array. The new array model was fabricated to receive focal spots with a distance of 40 mm from the first row to the focal plane under an off-axis illumination angle of 45°. In addition, this new design had a 97.5% fill-factor, a significant increase in the used light percentage. The previous design was only 76%. The optical performance of the high fill-factor EZP array was verified by using a focusing and imaging evaluation system. The results showed that its focusing ability was as well as the previous model with a distance of 780 µm between two adjacent focal points and an FWHM of 30 µm. In imaging performance, the high fill-factor EZP array remarkably demonstrated the ability to improve image brightness and image contrast compared with the previous EZP array, by enhancing the light utilization. Remarkably demonstrated the ability to improve image brightness and image contrast, by enhancing the light utilization.