The PDF lens (Edmund Optics, Barrington, NJ) used in this study had a focal length of +/- 100 mm, a diameter of 25 mm, and a thickness of 0.45 mm (Figure 3). Concentric rings were observed under a stereomicroscope (X20, SM-4TZ-30WY-16M3, Amscope, Irvine, CA). The converging lens for used to make the multifocal lens was an achromatic lens (chromatic aberration-free) with a focal length of +50 mm, diameter of 25.4 mm, and thickness of 11.5 mm (Thorlabs Inc., Newton, NJ). This converging lens had a back focal length of 43.4 mm from the flat surface of the lens (Figure 4). The 2 lenses were combined to create a multifocal lens. The experimental setting for measuring the multifocal function and optical quality of this lens was as described below.
1. Optical bench test
A white light-emitting diode (LED; 3-3/4 inch LED Square Plate for Microscopes, AmScope), USAF 1951 resolution target (2" x 2" Negative 1951 USAF Hi-Resolution Target, Edmund Optics), collimating lens (focal length 100 mm), 4 mm-diameter pupil, achromatic lens (focal length 50 mm), PDF lens (focal length +/- 100 mm), 8 mm-diameter pupil, and charge-coupled device (CCD) camera (acA1600-20uc, Basler, Ahrensburg, Germany) were arranged in a line (Figure 5). A polarizer was not used. The distance between the collimating lens with a focal length of 100 mm and the USAF resolution target was 100 mm. The PDF lens was fixed with tape in front of the lens mount of the achromatic lens (near the flat surface of the achromatic lens) and confirmed to be centered. The gap between the flat surface of the achromatic lens and the PDF lens was 2.0 mm. From the collimating lens to the CCD camera, all items were connected to a 30-mm cage system to eliminate the need for additional alignment. The LED and USAF resolution target were fixed to an XYZ translation stage (Thorlabs Inc.). While viewing the image on a monitor connected to the camera, the USAF resolution target was aligned at the axis of the 30-mm cage system by moving the stage.
1) Monofocal lens (achromatic lens only)
USAF resolution targets were photographed with only an LED, USAF 1951 resolution target, collimating lens (focal length 100 mm), 4 mm-diameter pupil, achromatic lens (focal length 50 mm), 8 mm-diameter pupil, and CCD camera without a PDF lens. The camera was moved back and forth to focus the image. When the clearest image was obtained, the distance between the flat surface of the achromatic lens and the CCD sensor was measured. A total of 8 images was taken around this location. Only when the distance between the achromatic lens’s flat surface and the CCD camera’s sensor was longer than 70 mm was the 8 mm pupil used in front of the camera to block unwanted light.
To quantify the quality of each image of the resolution target, we computed their cross-correlation coefficients. In general, a cross-correlation coefficient is used to quantify the similarity between 2 images.[6-8] To quantify the sharpness of each image, the similarity between the 2 images was compared using the cleanest image as a reference. Therefore, a cross-correlation coefficient that quantifies similarity can be used. As a reference template image for obtaining the cross-correlation coefficient, a middle rectangular area was selected and analyzed from a clear USAF resolution image (from group 2 to 7 elements; Figure 6). The cross-correlation coefficient between the test image f(x, y), including the blurred reference image and the sharp reference image t(x, y), can be obtained as follows.
To calculate the cross-correlation coefficient from the coordinates (u, v) of the test image, the center of the reference image was centered on these coordinates, and the pixels f(u, v) and t(u, v) subtracted by the mean value were multiplied pixel by pixel and normalized by dividing by its magnitude. The cross-correlation ranged from -1 to +1, and +1 indicated that the image was the same as the best query reference image. The cross-correlation indicated that the quality of the image decreased as the value of it decreased. The value of -1 indicated that the black and white pixels of the 2 images were inverted. When it was overlaid on the test image and scanned from the first row to the right column, the cross-correlation coefficient matrix from the first row to the last row was obtained as in equation (1). Among the coefficients of the matrix, the peak value was generally present in one place, and this value was the optimal cross-correlation coefficient. In addition, the best query-like image was obtained from the coordinate u and v information. The experimental results were as follows. The size of the actual test image was 1624 x 1234 pixels and the size of the reference image extracted from it was 474 x 445 pixels (Figure 6).
The cross-correlation coefficient of the acquired test image should be calculated with the image of the same magnification as the reference image. To this end, the magnification of the test image was calculated based on the number of pixels corresponding to the height of the rectangular border area, excluding the numbers of reference images. According to this magnification, the size of the test image was obtained again by a third-order polynomial interpolation method. In obtaining the cross-correlation coefficient with the test image considering magnification, it was possible to obtain the cross-correlation coefficient from most test images. In the scaled image, the partial image at the position where the peak of the cross-correlation occurs was displayed as a rectangular box. If the test image was severely blurred, however, it was not possible to find a matching region with only the maximum value of the correlation coefficient. In some test images, the cross-correlation coefficients were obtained manually. A curve was obtained by measuring the cross-correlation coefficient according to the distance from the flat surface of the achromatic lens to the sensor of the CCD camera, using MATLAB software (MathWorks; Natick, MA).
2) Multifocal lens (PDF lens + achromatic lens)
After the PDF was mounted, the experiment was repeated. First, the CCD sensor was positioned at 31.2 mm from the flat surface of the achromatic lens. (The distance between the flat surface of the achromatic lens and the CCD sensor was 31.2 mm.) Thirteen photos were obtained before the CCD sensor reached 91.2 mm from the flat surface of the achromatic lens. (Due to the thickness of the achromatic lens, thickness of the C-mount adapter, and flange of the C-mount camera [17.526 mm], the CCD sensor could not be closer to the flat surface of the achromatic lens than 31.2 mm.) Only when the distance between the achromatic lens’s flat surface and the CCD camera sensor was greater than 70 mm could the 8-mm pupil be used in front of the camera to block unwanted light. At this time, the clearest (in focus) image among the photos obtained with the above monofocal lens (achromatic lens only) was used as a reference image for calculating the cross-correlation coefficient.
During the experiment, the LED brightness and camera settings (exposure time, International Organization for Standardization [ISO], gamma value, white balance, etc.) were not changed.
2. Digital single-lens reflex camera test
The multifocal function and optical quality of a multifocal lens (PDF lens + converging lens) in various conditions were tested using a digital single-lens reflex (DSLR) camera (D610, Nikon, Tokyo, Japan; Figure 7). Because the flange focal distance of the DSLR camera was 46.50 mm, an f = 50 mm achromatic lens could not focus light at a DSLR camera sensor, so an f = 75 mm monofocal lens (back focal length 70.3 mm) was used for the monofocal lens test. The system was made of a 4-mm pupil, achromatic lens (focal length 75 mm), and DSLR camera. They all were connected to a 30-mm cage system to eliminate the need for additional alignment. A polarizer was not used. Focus was achieved by adjusting the distance between the camera and the achromatic lens. When a far object more than 6 m away appeared clear, the achromatic lens was fixed at the cage system. After focusing, the ambient light was shielded with black tape, and objects at far and near distances were photographed or recorded as videos.
To test the multifocal lens, a 4-mm pupil, achromatic lens (focal length 50 mm), focal length +/- 100 mm PDF lens, and a DSLR camera were used. The PDF lens was fixed with tape in front of the lens mount of the achromatic lens (near the flat surface of the achromatic lens) and it was confirmed to be centered. A polarizer was not used.
Focus was achieved by adjusting the distance between the camera and the multifocal lens. At this time, the multifocal lens was positioned so that the longer focus of the multifocal lens was located at the sensor of the camera. After focusing, the ambient light was shielded with black tape, and objects at far and near distances were photographed or recorded as videos.
1) Far distance
During the day, a parking lot was photographed with a DSLR camera, and this was repeated with a monofocal lens and a multifocal lens. Using a tripod, we attempted to capture the same view with both the monofocal and multifocal lenses.
2) Near distance
To test multifocal function, the Early Treatment Diabetic Retinopathy Study (ETDRS) chart (ETDRS 2000 Series chart "2" [Precision Vision, La Salle, IL]) was used as the near target. The ETDRS chart started at 385 mm from the convex surface of the achromatic lens. The ETDRS chart was brought closer to the DSLR camera until it reached 40 mm, i.e., the distance between the convex surface of the achromatic lens and the ETDRS chart was 40 mm; Figure 7.) The approach toward the camera was recorded as a video. General stand lighting was used.
3) Far and near distance
To test the multifocal function in the daytime, the ETDRS chart at near distance was recorded as a video right after recording a distant parking lot. This was repeated for the monofocal lens and the multifocal lens.