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Abstract
In this paper, a quasi-simultaneous multi-focus imaging technique named simulfocus imaging is reported. This technique was developed for measuring an entire object distributed in the depth direction beyond the depth of field (DOF) with high resolution in a single shot. Simulfocus imaging can acquire multiple focal planes in one shot by synchronizing a tunable acoustic gradient index (TAG) lens and a lock-in pixel image sensor. The TAG lens is a tunable-focus lens whose focal position can be changed at a high speed of several tens to several hundreds of kilohertz. The lock-in pixel image sensor is a special image sensor that can execute multiple exposures at an arbitrary timing during a single shooting. The sensor includes a number of photoelectron storage units in each pixel, and the units where the photoelectrons generated by each exposure are stored can be freely selected. Since an image can be acquired for a single storage unit, and the lock-in pixel image sensor has a number of storage units, the lock-in pixel image sensor can acquire multiple images in one shot. By assigning a specific exposure timing to each unit and synchronizing the exposure timing with the focus fluctuation of the TAG lens, it is possible to simultaneously acquire images in different focal planes. To evaluate the system, we conducted experiments to show the effectiveness of simulfocus imaging in microscope and telescope configurations. From the experimental results, it was confirmed that simulfocus was effective in both configurations.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Large numerical apertures are required for optical systems that require high resolution, such as microscopes [1] and telescopes. Therefore, these optical systems have the property that the depth of field (DOF) becomes shallow. In such optical systems with a shallow DOF, it is important to focus on the position to be observed; otherwise, the resolution will be significantly reduced due to blurring.
If the object is distributed in the depth direction beyond the DOF, it is impossible to measure the entire object with high resolution in one shot. To overcome this difficulty, it is necessary to (i) measure multiple images while changing the focus, or (ii) reduce the aperture to increase the DOF so that the entire object is in focus. However, there are problems with these approaches: (i) loses the simultaneity of measurement between different focal positions, and (ii) cannot avoid a reduction in resolution due to a decrease in the numerical aperture.
One approach to overcome these difficulties is to use holography, which records all information of the incident light, including the intensity and wavefront distributions, so that images with arbitrary focal depths can be generated by computation [2,3]. Light field imaging is a similar technique, but it approximates the incident light as a set of light rays and synthesizes an image from the measured set of light rays [4,5]. The set of light rays are captured using two or more cameras or a plenoptic camera. Both techniques tend to require a considerable amount of computation to generate an image with a given focal length.
Tunable-focus lenses are considered to be promising key devices for reducing the timing mismatch with approach (i) above. High-speed focus control using tunable-focus lens devices has been studied [6–11]. However, the response time of existing tunable-focus lenses is a few milliseconds, which is not fast enough when measuring at high frame rates. A resonant tunable-focus lens called a Tunable Acoustic Gradient index (TAG) lens, based on a faster focus-tuning principle, has appeared in recent years [12–14]. The TAG lens has a structure in which a liquid is sealed in a cylindrical container, and a refractive index distribution is formed by generating compression waves in an axially symmetric resonance mode. As a result, the structure functions as a lens. The vibration of the refractive index distribution directly becomes the vibration of the focal length. The resonance frequency is very high, from several tens to several hundreds of kilohertz. However, since the liquid is vibrated by resonance, the optical characteristics cannot be fixed at a specific focal length. With a normal image sensor, an image is formed by scanning the focus. In order to acquire information on a specific focus position from a TAG lens, an image sensor that can execute exposure only when the focal length of the TAG lens reaches a specific focus position is required. However, this approach is not practical because only a very dark image can be acquired with such short exposure under normal illumination conditions.
As one solution to this problem, a temporally coded exposure (TeCE) camera [15–17] has been reported; this image sensor can acquire information on a specific focus position from a TAG lens. The TeCE camera can perform multiple short exposures at any time while taking one image, and can accumulate the photoelectrons generated by each exposure. By synchronizing the exposure of the TeCE camera and the focus tuning of the TAG lens, an image at a specific focus position can be acquired with a practical brightness level. Also, the TeCE camera can acquire an image with an arbitrary focal length in a frame-by-frame manner, since the focal length can be selected just by changing the exposure timing electrically. However, there is a residual timing mismatch between image acquisitions even with the TeCE camera, depending on the frame period, since the TeCE camera cannot acquire multiple images in one shot.
As an image sensor that can solve this timing mismatch problem, Seo et al. have developed the so-called lock-in pixel image sensor that can acquire multiple images in a single shot [18–20]. The lock-in pixel image sensor has two features not found in ordinary image sensors: One feature is that a pixel has multiple photoelectron storage units called taps, and it is possible to freely select which tap stores the photoelectrons generated by each exposure. The other feature is the ability to perform multiple exposures at an arbitrary timing while taking a single image, and to form a multi-exposure image by integrating them. Since the lock-in pixel image sensor used in this paper has four taps, four images with different exposure timings can be obtained in a single imaging shot.
In this study, we propose a quasi-simultaneous multi-focus imaging method that can measure images at multiple focuses at almost the same time; we call this system “simulfocus imaging”. Simulfocus imaging consists of two main elements: a TAG lens and a lock-in pixel image sensor. To verify the effectiveness of simulfocus imaging, we performed experiments to acquire multiple focal planes quasi-simultaneously in a microscope configuration and a telescope configuration. From the experimental results, it was confirmed that Simalfocus imaging was effective in both configurations.
2. Simulfocus imaging
2.1 Synchronization between TAG lens and lock-in pixel image sensor for simulfocus imaging
The objective of simulfocus imaging is to measure images quasi-simultaneously at different focal positions. In this study, simulfocus imaging was realized by using two main components: the TAG lens and the lock-in pixel image sensor, as described above.
Figure 1 shows a conceptual diagram of simulfocus imaging. This figure represents the synchronization between the focus fluctuation of the TAG lens and the multiple exposures of the lock-in pixel image sensor. Note that the case where the number of taps of the lock-in pixel image sensor is four is shown as an example. The TAG lens outputs a synchronization signal when its refracting power is the strongest (the focal length is the shortest). The resonance frequency and period of the TAG lens are known in advance. In this study, synchronization between the Lock-in Pixel image sensor and the TAG lens is achieved by inputting a synchronization signal to a field-programmable gate array (FPGA) and executing exposure after an arbitrary delay from the input of the synchronization signal. That is, the delay control is equivalent to controlling the exposure timing. By setting a different delay for each tap of the $n$-tap lock-in pixel image sensor, $n$ different focal planes can be acquired quasi-simultaneously. Furthermore, the resonance frequency of the TAG lens is several hundred times faster than the frame rate of the lock-in pixel image sensor, so that multiple exposures can be performed during one shooting with a timing mismatch on the order of microseconds. As a result, images with both small timing mismatch and sufficient brightness can be obtained despite the short exposure duration.
Fig. 1. Conceptual diagram of simulfocus imaging. Note that the TAG lens is scanning between convex and concave lens at high speed. For the sake of clarity, this figure is represented only when the TAG lens is a convex lens.
2.2 Construction of experimental systems
In this study, experimental systems connected to a microscope system and a telescope system were constructed to evaluate the effectiveness of simulfocus imaging. Figure 2 shows the constructed experimental systems, and Fig. 3 shows the photographs of them. As shown in Fig. 2(a) and Fig. 2(c), the TAG lens was installed in a relay lens system. On the other hand, in the experimental system for the telescope configuration, the TAG lens was installed in front of the telephoto lens without using a relay lens system, as shown in Fig. 2(b) and Fig. 2(d). Since the angle of view of the telescope configuration was small, direct coupling worked well.
Fig. 2. Configuration of the constructed experimental systems, in terms of each measurement configuration and its light path diagram. In (c), OL is an objective lens, TL is a tube lens, L1 and L2 are lenses for the relay optics with focal lengths of 100 mm (L1) and 70 mm (L2), TAG is the TAG lens, and I is the lock-in pixel image sensor. In (d), TAG is the TAG lens, L3 is a telescope lens, and I is the lock-in pixel image sensor.
3. Experiments and discussions
This section describes experiments conducted to evaluate simulfocus imaging by using the constructed experimental systems described above. Three kinds of evaluation experiments were conducted, as follows. First, simultaneity, meaning that the lock-in pixel image sensor could acquire multiple images in one shooting, was verified. Second and third, the results of simulfocus imaging with the microscope and telescope configurations, respectively, are shown.
Here, the devices used in the following experiments and their settings are described. The lock-in pixel image sensor used in this study had four taps, and its frame rate was 100 fps. The frame resolution of each tap was 132$\times$82 pixels. The TAG lens used in this study was a TAG LENS 2.5$\beta$ (TAG OPTICS), and its resonance frequency was 69 kHz. The detailed experimental conditions are described in each experimental section below.
3.1 Verification of simultaneity
To verify whether the lock-in pixel image sensor could acquire four images in one shooting, simultaneity of the system was verified. This experiment used the telescope configuration and was executed by capturing LED switching with the lock-in pixel image sensor. In particular, repeated turning on and off of the LED for 10 ms was captured by the lock-in pixel image sensor. If quasi-simultaneity between four images in the same frame were established, the on/off states of the LED in the captured images should be the same between the four images.
The telescope lens used in this experiment was a FUJINON TV LENS 75mm (FUJIFILM). The exposure timings for the taps of the lock-in pixel image sensor were 0.0 $\mu$s, 1.2 $\mu$s, 2.0 $\mu$s, and 3.6 $\mu$s after the synchronization signal of the TAG lens, and the exposure duration was set to 1.0 $\mu$s.
Figure 4 shows the results for verifying simultaneity. The frame rate of the lock-in pixel image sensor was 100 fps; i.e. it took 10 ms for one shooting. As shown in Fig. 4, the LED was switched on and off every 10 ms with every tap. Therefore, the quasi-simultaneity of the lock-in pixel image sensor was verified with a time accuracy of millisecond order.
3.2 Experimental results for microscope configuration
Second, simulfocus imaging was evaluated in the microscope configuration. In this experiment, a Ronchi ruling glass slide (40 line pairs per mm) was used as the measured object, which was installed at a tilt angle of 16.4 degrees, as shown in Fig. 5. The reason why the object was tilted was to make it obvious that different focus positions could be acquired quasi-simultaneously by simulfocus imaging. The microscope used in this experiment was IX71 (OLYMPUS), and an UplanSApo 10x/0.40 objective lens (OLYMPUS) was used. The amplitude of vibration of the TAG lens was set to 45%. Note that the refractive power was about 1.5 diopter when the amplitude was 47%. The exposure timings for the taps of the lock-in pixel image sensor were 0.000 $\mu$s, 2.352 $\mu$s, 3.648 $\mu$s, and 6.000 $\mu$s after the synchronization signal of the TAG lens. The exposure duration was set to 0.200 $\mu$s.
Figure 6 shows the captured images of the Ronchi ruling and their contrast profiles. Comparing the acquired images at each tap, it was confirmed that the focus position was different for each image. In addition, to quantitatively evaluate the degree of focusing, the contrast of each image was calculated. In this study, Michelson contrast was used as the criterion for the degree of focusing. The contrast calculation procedure was as follows. First, the pixels of the center column were extracted from each image. Second, the extracted pixels were divided into 6 pixels in order from the top, and the maximum and the minimum pixel values were obtained from these 6 pixels. Then, the contrast, $C$, was calculated as follows:
where $L_{max}$ and $L_{min}$ denote the maximum and the minimum pixel values, respectively. The above calculation was applied to all extracted pixels, and the obtained profiles are shown in the lower row of Fig. 6. Comparing the contrast from TAP1 to TAP4, the high-contrast position changed from top to bottom in the image. Therefore, it was confirmed that different focal planes could be acquired for each tap. From the above results, simulfocus imaging successfully obtained four images at different focal lengths quasi-simultaneously with the microscope configuration.Fig. 6. Acquisition results of tilted Ronchi ruling glass slide. The upper row shows the image acquired by each tap, and the lower row shows the contrast profile in the vertical direction in each acquired image.
Assuming that full width at half maximum (FWHM) of contrast profile shown in Fig. 6 is an evaluation criterion of DOF, it can be confirmed that DOF of each focal plane is almost same. FWHM of TAP3 shown in Fig. 6 was equal to 39 pixels. DOF could be calculated from stripe widths and tilt angle of the Ronchi ruling and it was 32.2 $\mu$m. In addition, it has been confirmed that DOF has been comparable at any exposure timings in the microscope configuration [15]. In other words, DOFs of other taps are also about 32 $\mu$m. The depth position of each tap could be estimated from contrast profiles of Fig. 6. When the depth position where the exposure timing was 0.000 $\mu$s was 0.0 $\mu$m, the depth positions corresponding to 2.352 $\mu$s, 3.648 $\mu$s, and 6.000 $\mu$s were 8.3 $\mu$m, 28.9 $\mu$m, and 49.6 $\mu$m, respectively. Since the depth between TAP1 and TAP4 was about 50 $\mu$m, the focus range was from -16 to 66 $\mu$m. Therefore, the entire DOF was expanded by simulfocus imaging in the microscope configuration.
3.3 Experimental results for telescope configuration
As the third experiment, simulfocus imaging was evaluated in the telescope configuration. In this experiment, the measurement objects were cards displaying numbers, held by 4 persons, as shown in Fig. 7. The telescope lens used in this experiment was a FUJINON TV LENS 75mm (FUJIFILM). The amplitude of the TAG lens was set to 32%, which was equivalent to an amplitude of 1 diopter. The exposure timings of the taps of the lock-in pixel image sensor were 0.000 $\mu$s, 1.940 $\mu$s, 2.840 $\mu$s, and 3.624 $\mu$s after the synchronization signal of the TAG lens, and the exposure duration was set to 0.500 $\mu$s.
Figure 8 shows the results acquired with the configuration in Fig. 7 using the telescope experimental system. The lower images in this figure show images obtained by applying an edge detection filter to the upper images, as the evaluation criteria of the degree of focus. In the edge detection processing in this study, after applying a Laplacian filter to the image, the values after filtering were squared and divided by 255. As shown in Fig. 8, the edge of the card displaying "1st" was detected in the edge detection result of TAP1. In the same manner, the edges of the cards displaying "2nd", "3rd" and "4th" were detected in TAP2, TAP3, and TAP4, respectively. Therefore, different focal planes could be acquired for each TAP. From the above results, it was confirmed that simulfocus imaging was also effective in the telescope configuration. For the expansion of DOF in the telescope configuration, when focusing on an object at 3.6 m, the other objects were out of focus as shown in Fig. 8. Thus, it was confirmed that DOF was expanded as a whole by 4 focal planes acquired in different focus positions.
Fig. 8. Acquisition results for telescope configuration shown in Fig. 7. The upper images are the images acquired by each tap, and the lower images show the results of applying an edge detection filter to the upper images.
As shown in Fig. 2(d), the telescope lens was directly connected with TAG lens in the telescopic configuration and the telescope lens L3 was focused on infinity. Therefore, the distances between the TAG lens and focused object are estimated as the focal length of TAG lens. The estimated refractive powers of TAG lens were about 0.27, 0.17, 0.10, and 0.056 diopter in order of TAP1 to TAP4. On the other hand, assuming that the amplitude of refractive power of the TAG lens $A$ is 1.0 diopter and fluctuation cycle $T$ is 14.5 $\mu$s, the refractive power $D$ at time $t$ can be estimated as follows:
The refractive powers estimated by the above equation were 0.5, 0.44, 0.39, and 0.33 diopter in order of TAP1 to TAP4 and were different from the refractive power estimated by focal length of TAG lens. The possible cause are (i)amplitude reduction due to low temperature and (ii)delay inherent in synchronization signal of the TAG lens. The refractive power of the TAG lens especially depends on sound speed in a liquid and sound speed also depends on temperature [14]. In particular, since this experiment was conducted when it was winter in Japan, the outside temperature was as low as 5 to 10 degree Celsius. Therefore, it was speculated that this difference was due to the deviation from the operating temperature of the TAG lens.3.4 Experiment for measuring moving objects
To show the effectiveness of simulfocus imaging in practical applications, we demonstrated the measurement of moving objects. Figure 9 shows the measurement results of moving objects in both configurations.
Figure 9(a) shows the temporal change of the images acquired by simulfocus imaging. The measured objects were Chlamydomonas algae cells, and a 50x objective lens (UMPLFL50X; OLYMPUS) was used. Three-dimensional movement of the Chlamydomonas could be measured by capturing continuous images with simulfocus imaging. It could be confirmed that two cells existing at different depths were focused simultaneously at TAP1 and TAP3 at 200 ms.
Fig. 9. Temporal change of image acquired in 2 kinds of configurations. These temporal changes are shown in Visualization 1.
Figure 9(b) shows the temporal change of the images acquired by simulfocus imaging in the telescope configuration. The measured object was a person approaching from a distance. As shown in Fig. 9(b), the focus was on TAP4 when the person was far away. As the person approached, the focus position of the person changed from TAP4 to TAP3, TAP2, and then TAP1.
Therefore, it was confirmed that simulfocus imaging could quasi-simultaneously acquire multiple focal planes of moving objects.
3.5 Discussions
From the above experimental results, it was confirmed that simulfocus imaging proposed in this paper could quasi-simultaneously acquire 4 focal planes using the TAG lens and the lock-in pixel image sensor. The focus fluctuation of TAG lens was set to 69 kHz and the frame rate of the lock-in pixel image sensor was set to 100 fps (100 Hz) in the experiments. The fluctuation frequency of the TAG lens is about 1000 times higher than the frame rate of the lock-in pixel image sensor. simulfocus imaging can obtain focal planes with sufficient brightness by multiple exposure.
Then, if a high speed camera whose frame rate is as well or higher than the fluctuation of TAG lens is used and the acquired frames are accumulated, is it possible to do the same as simulfocus imaging? As an example, if a high speed camera with 100 kfps can acquire 1000 frames during 10 ms and an exposure can be executed for each 250 frames at each focus position, can the same as the 4 taps simulfocus imaging be realized? The answer to this is no. The image sensors quantize the charge with an A/D converter and convert it into digital information each time a frame is acquired. However, since the exposure duration of one shot is very short, the luminance value cannot be measured unless it is an extremely sensitive image sensor. In other words, no matter how many times the frame whose brightness is equal to 0 is accumulated, the brightness of accumulated frame is 0. Hence, simulfocus imaging could be realized by coupling between TAG lens and the lock-in pixel image sensor.
Furthermore, the potential and limit of the lock-in pixel image sensor and the simulfocus imaging are discussed in terms of (i)temporal resolution of exposure, (ii)the number of taps, (iii)the relationship between the number of taps and the number of focal planes, and (iv)the relationship between TAG lens period and the exposure time of the lock-in pixel image sensor. In (i), the lock-in pixel image sensor can control exposures with an accuracy of 10 ps [19]. In (ii), the taps of the lock-in pixel image sensor are formed in the pixel of the image sensor. Therefore, the taps can be increased depending on the design of the image sensor. However, if the number of taps is increased, the area required for one pixel is increased, and the number of pixels of the entire image sensor is decreased. Hence, it is practical that the number of taps is from 2 to 8 [20]. In (iii), the number of focal planes that can be acquired by the lock-in pixel image sensor at one shot depend on the number of taps.. If focal planes that are more than the number of taps will be acquired, it is necessary to divide focal planes into multiple frames. For example, if 8 focal planes are acquired by 4 taps lock-in pixel image sensor, these planes must be acquired in 2 frames. In order to change the number of taps of the lock-in pixel image sensor, it is necessary to fundamentally change the hardware design of it because the taps are formed in the pixel of the image sensor. In (iv), the focus fluctuation of TAG lens is much faster than the lock-in pixel image sensor. However, the number of focal planes that can be acquired quasi-simultaneously is limited by the number of taps.
4. Conclusion
In this paper, we proposed simulfocus imaging, which measured images at multiple focuses at almost the same time. The simulfocus imaging system consisted of two main elements: a TAG lens and a lock-in pixel image sensor. The TAG lens, which is a tunable-focus lens, could vibrate the focus position at high speed. The lock-in pixel image sensor had multiple taps in each pixel and could acquire multiple images quasi-simultaneously during one shooting. Simulfocus imaging was implemented by synchronizing the TAG lens with the lock-in pixel image sensor. Simulfocus imaging experimental systems were constructed for two acquisition configurations: a microscope configuration and a telescope configuration. Experiments were performed using these systems. The experimental results showed that different focal planes could be acquired with each tap in both configurations. Therefore, the effectiveness of simulfocus imaging was confirmed.
Funding
Accelerated Innovation Research Initiative Turning Top Science and Ideas into High-Impact Values (JPMJAC1601); Ministry of Internal Affairs and Communications (181608001); Japan Society for the Promotion of Science (18H05240); Ministry of Education, Culture, Sports, Science and Technology (Regional Innovation Ecosystem Program).
Disclosures
The authors declare no conflicts of interest.
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