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Abstract
The LAser raDAR (LADAR) system designed in this study shows a ghost pattern around the object image when operated. The system contains 4 wedge prisms, each with different rotational directions and speeds. Therefore, an efficient and thorough analysis method was established. Ray path analysis was performed, and categorized, for every instantaneous case sampled using a backward ray tracing method. The rays’ flux and directions were accumulated according to their path histories. This backward ray tracing was performed repeatedly with different neutral density (ND) filter orientations, until no measurable ghost radiance remained in the field of regard (FOR): a tilt angle of 5°. The ND filter was replaced with a mechanical vignette. Subsequently, the ghost flux was 21% of the total accumulated point cloud, coinciding with the actual measurement of 19%. The final image has significantly improved resolution and shows no ghost reflections where they were previously.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The LAser raDAR (LADAR) system, designed in this study, is an active system which collects the returning signal of a self-generated laser pulse emitted from a laser module, and forms a point cloud with range information as shown in Fig. 1. The LADAR system contains 3 optical modules: the laser transmitting channel module (TCM); the signal receiving channel module (RCM); and the scanner channel module (SCM), whose optical path is shared by the RCM and TCM to overcome the narrow field of view (FOV) due to the limited resolution of the focal plane array (FPA) [1].
The optical system of the RCM has two planar optical components: the ND filter and the bandpass filter. Initial stray light analysis has previously been performed to minimize the ghost image signal, showing it is enough to eliminate internal reflections, from the planar optical components, by tilting the ND filter by 2° [2]. Implement this refracted the ghost paths but ghost signatures still remained in the system, as significant as the signal shown in Fig. 2(b) [3].
Fig. 2. The ghost pattern of the final image: (a) actual image of the object and (b) the corresponding pseudo color map showing distance from the optical system aperture, including: (1) a ghost pattern around the thin antenna and unresolvable guardrail, and (2) the ghost image of the bottom floor.
Given that the TCM and RCM share the optical path of the SCM, stray light analysis can be performed on two aspects. The first is the internal reflection of the laser signal fired from the TCM, and the second is the internal reflection of the incoming signal to the RCM. The paths of the laser signal fired from the TCM were analyzed, confirming that the rays reflected from the SCM do not reach the active area of the FPA but do reach the mechanical structures of the RCM [4].
If the RCM comprises conventional stationary optical components, such as an aberration corrector, beam splitter and variable FOV shifter, its ghost problem could easily have been avoided [5–10]. However, it is highly complicated to analyze the internal reflection paths of the incoming signal to the RCM comprising 2 sets of Risley prism wedges with different rotational directions and rates. Given that the chief ray of the incoming signal is altered by operation of the SCM, the nominal incoming ray path, at any instantaneous moment, can be the ghost signal path at a different instantaneous moment. Thus, ray path analysis should be performed over a series of instantaneous moments. The number of instantaneous moments required will be dependent on the movement of the SCM and the laser pulse rate of the laser module. An alternative solution, to simplify the SCM operation concept, a drum scanner may be used to widen the FOV to the FOR, with minimum ghost reflection. However, it requires more volume than that of the Risley prism scanner, and it is harder to produce a complex scanning pattern compared to that of the Risley prism scanning system [11–14].
There are two disadvantages to the classical ghost path analysis method. The first is that non-sequential ray tracing software can only handle a single instantaneous configuration. For instance, the ray path intersecting a prism can be calculated using classical optics formula, such as Snell's law. Though, with the aid of modern computational power, the calculation can only be performed for the optical component in a specific orientation, in a single instantaneous moment. This results in a large total number of cases that must be analyzed [15]. The ghost path of the drum scanner can be calculated in this intuitive way since the scanning pattern of the drum scanner involves simple 2-dimensional motion [13]. However, it is highly complex to calculate the ghost path of our Risley prism scanning system with 4 stacked prisms, each with different rotational directions, speeds and slant angles, since the optical paths are refracted continuously with the operation of the SCM. Thus, it is crucial to perform ghost analysis in accordance with the operation of the SCM.
The second is that it is neither intuitive nor continuous when the ray path is refracted or shifted by changing the orientation of optical components, because the ghost irradiance suddenly disappears from the FPA. Although this can show that the problem has been resolved, it is hard to recognize how the paths have been shifted and where the rays finally sit. Furthermore, it is still possible that these paths may be refracted to reach the FPA by other non-stationary optical components, when they reach a certain orientation, as shown in Fig. 3. The signal moves according to the rotation of the SCM. When it reaches a certain position, the ghost appears immediately adjacent to the signal, as shown in Fig. 3(g). Although the signal is not present from the Fig. 3(j) onward, the ghost still exists and moves in the opposite direction to the signal, as shown in Fig. 3(j) - Fig. 3(n).
Fig. 3. Sequential signal images as the scanners of the SCM rotate. . The signal and ghost images are indicated by arrows. The central cross indicates the center of the FPA. The subfigure label (a) through (n) show the sequence of events as the scanners rotate.
To perform ghost analysis of a system with non-stationary optical components, overcoming these conventional limitations, the following steps were taken. First, the operation concept of the SCM was taken into consideration for the ghost analysis scheme. Then the rays were traced backward from the FPA to the system entrance aperture. The rays were collected at a dummy surface, at the aperture entrance, and categorized into ray path groups according to their individual direction and split generation. After categorization, the radiant intensity and flux distribution can be calculated in angle space according to each ray path group. In this manner, the refracted paths can be traced continuously, even when the ray path is refracted off the FPA by a change in orientation of any optical component.
The optical design and methodology of the backward ray path analysis are explained in section 2. The backward ray path analysis results are presented in section 3. The results of the accumulated radiance signatures are also presented in this section, including error analysis. As a solution of this residual ghost radiance, implementing the mechanical vignette is explained in section 3, with its expected improvement. The results of implementing the mechanical vignette are discussed in section 4. Our conclusion, with the significantly improved image of the current LADAR system, is given in section 5.
2. Optical design and methodology
2.1 Optical design
The optical modules of our LADAR system are the TCM, RCM and SCM. A schematic showing the optical layout of these optical modules are shown in Fig. 4.
Fig. 4. Optical layout schematic of the TCM, RCM and SCM. The blue dashed line indicated the optical path through the modules. The RCM is comprised of lens 1 (L1), mirror 1 (M1), mirror 2 (M2), lens 2 (L2), bandpass filter, ND filter, lens 3 (L3) and FPA.
The wedge scanner module consists of 2 scanner pairs, each consisting of two identical wedge scanners. These pairs are responsible for vertical and horizontal scanning, widening the FOV 0.25°×0.25° to the FOR 2.3°×1.3°. The RCM consists of three lenses, two mirrors, one bandpass filter and one ND filter replacing Etalon used in the earlier design [1]. An anti-reflection coating was applied to each lens surface to minimize ghost reflection irradiance of the signal. A brief specification of the scanners and RCM are described in Table 1 [1].
Table 1. Basic specifications of the SCM and RCMa optical components.
A narrow bandpass filter was used to block irradiance for non-signal wavelengths. The bandpass filter has a full-width at half-maximum of 3.0 nm and a central wavelength of 1560 nm. In total, there were 5 ND filters with a tilt angle of 2°, each of which were mounted on the ND filter wheel. Due to the limitation of controlling laser power and FPA sensitivity, various ND filters were inserted to control the transmittance of the system.
The spot diagram performance test of the RCM is shown in Table 2. Given that the system fires laser pulses with a single wavelength and collects point coordinate data from the reflected and scattered rays from the object, the spot diagram performance is a key design factor. It is often far more important than any other optical feature. The root mean square (RMS) spot semi-diameter of each field is smaller than 22 µm in every field, smaller than the individual pixel width of 100 µm.
Table 2. Spot diagram of the RCMa. The red spot indicates 1550 nm and the blue 1570 nm respectively.
2.2 Analysis method
The backward ray tracing ghost analysis method can be established using two underlying principles. The first is that the incoming ray path of the major ghost image consists of 2nd generation split rays, and their paths are reversible [16]. Although they have higher irradiance, 1st generation split rays are not a major contributor because their direction is opposite to that of the parent ray. Also, 3rd generation (and higher) split rays have flux that is too low to contribute to the stray light signature [2,5].
The second is that the accumulated radiance, in each analysis case, can represent the signal and ghost irradiance of the combined image mapping the full FOR when traced backward, from the FPA at the front of the optical system. Note that an FPA signal mapped in a spatial coordinate system as irradiance, can be displayed in an angular coordinate system as radiance. Thus, an irradiance map of a combined FPA image in a spatial coordinate system, according to the operation of the scanner, can represent FOR in an angular coordinate system. A basic scheme of the analysis is shown in Fig. 5.
First, a dummy plane should be defined in front of the system, to collect rays starting from the FPA in step 1. An adjustment of the orientations of the ND filter and wedge scanners, in the SCM module, should be made in step 2 and 3, respectively. Then ray tracing should be performed from the ray bundle with the Lambertian distribution created on the FPA, generating up to 2nd generation split rays by Snell’s Law and Fresnel equations, as in step 4. A basic scheme of the ray tracing is illustrated in Fig. 6.
Fig. 6. Basic scheme of backward ray tracing in the nth and (n + 1)th instantaneous orientation. The ray vectors and the rotational optical component belong to nth instantaneous orientation are highlighted in gray color. The ray vectors in nth instantaneous orientation are illustrated in solid lines and the ray vectors in (n + 1)th instantaneous orientation in dashed lines. l: the initial ray number, k: the total number of surfaces from the FPA to the ray capturing dummy surface, m: split order, 0 or 2, n: the nth instantaneous sampled orientation, t: the number of surfaces intersected to reach the dummy surface, s: the surface number where the split occurred when m = 2, or 0 when m = 0
The fixed optical component represents stationary optics, such as the RCM, while the rotational optical component about the optical axis represents the SCM in Fig. 6. The split order m can be either 0 or 2, given that the rays for an odd split order propagate in the opposite direction and cannot reach the ray capturing dummy surface. The 4th (and higher) generations of the split rays have negligible flux (<6.25−10 of the initial ray flux), when the reflectance of the surface is as small as 0.5%. Then the ray vector R can be expressed in Eq. (1) below:
After the ray tracing is complete, the collected rays can be categorized into a $2 \times l$ matrix ${M_{m,n,t,s}}$, according to their split order, the number of surfaces intersected to reach the dummy surface, and the surface where the split occurred in every instantaneous sampled orientation, as shown in Eq. (3) below. This represents step 5.
The flux of each matrix and categorization is completed using Eq. (5) and Eq. (6), respectively. During which, calculations for the next instantaneous sampled orientation of the SCM can be performed until the calculations for all the instantaneous cases have been completed.
Fig. 7. Point cloud plotted in the αβ plane of an angular coordinate system: (a) a ghost point cloud penetrates the FOR, and (b) prior ghost point clouds are pushed away from the FOR.
To calculate the instantaneous orientation of the scanner at a specific moment, the repetition rate of the laser and the rotational speed of each scanner are needed. When the repetition rate of the laser RL, the rotational speed of the horizontal scanner VHS, and the rotational speed of the vertical scanner VVS are recorded in Hz, then the angular position of each scanner, AV1, AV2, AH1 and AH2, can be calculated as an angle for the Nth sampled moment, as in Eqs. (9)–(12):
When the image rate of the system in real time is F Hz, the number of images that should be accumulated in a single frame, at the system level, NImage Single Frame, can be described as in Eq. (13):If a single image is sampled every Mth image, the total number of cases for analysis, Nfinal, can be calculated using Eq. (14):
A brief analysis of the FOR was performed to calculate an appropriate value of M. Given that the gap between this and the nearby instantaneous FOV is maximized at the center of the accumulated FOR image, the value of M is chosen so that this gap is filled by a neighboring instantaneous FOV. Also, M must be a common denominator of NImage single frame, so that Nfinal is an integer. As a result, a total of 250 analysis cases were identified for a single frame image. With the tilt angle of the ND filter being between 0° and 6°, ray tracing was performed in a total of 10,500 (250×6×7) individual cases.Figure 8 shows the actual continuous wave (CW) laser projected on the wall by the scanner. The line image of Fig. 8(a) signifies the movement of the chief ray when the SCM is in operation. Figure 8(b) is the image created in ray tracing software, implementing the operation concept of the receiving optics module and the scanner module. It is considered that the operational concept is well implemented in the analysis scheme shown in Fig. 8.
Fig. 8. (a) The scanning pattern of the wedge scanner module created by the actual CW laser. (b) The footprint pattern of the wedge scanner module created by a ray tracing simulation.
The presented methodology has advantages compared to conventional stray light analysis methods. First, this methodology can simulate the operation of a scanner with errors limited to the mechanical implementation. When tracing rays forward from the aperture to the FPA, the scanned image data should be re-coordinated according to the orientation of the scanner in post-processing to see the whole FOR image combined from the individual FOVs, like making a mosaic. This may increase the ray tracing error, since the positional error induced by the re-coordinating algorithm may be introduced. However, our ray tracing method is free from these errors since it only implements the change in the mechanical and optical orientation. Second, the result is continuous and intuitive, even when the ghost path is refracted, so that the ghost image is pushed away from the FPA in the angle space. The ghost image still exists outside the FOR region, even when their paths are pushed away from the FOR in the angular coordinate system.
3. Analysis results
3.1 Instantaneous ghost radiance regarding the FOR
To perform backward ray tracing, a planar Lambertian ray source large enough to fill the exit pupil was created on the FPA, towards the entrance aperture of the optical system, as shown in Fig. 9. The rays were created on the FPA surface and propagated until they met the ray capturing dummy surface.
Fig. 9. Ray source created on the FPA and its propagation direction in the backward ray tracing scheme.
The major parameters used in the ray tracing are shown in Table 3. The refractive index of BK7 and silica have been sourced from the glass catalog of CODE V, and Borofloat is from the manufacturer Thorlabs. The mechanical components were modeled with the 100% absorption.
Table 3. Backward ray tracing parameters.
The measured reflectance and transmittance of each ND filter are shown in Table 4. Although ND filters are absorptive with little reflectance, each ND filter showed a relatively high reflectance.
Table 4. Reflectance and transmittance of the ND Filters.
When the rays are traced on a system level, including the wedge scanner module, they must be categorized according to the FOR of the system. Figure 10 shows the radiance distribution of a single instantaneous case, in an angular coordinate system. Figure 10(a) shows the radiance distribution when the ND filter is placed normal to the line of sight (LOS) of the receiving optics module, and Fig. 10(b) shows the radiance distribution when the ND filter is tilted by 2° to the LOS.
Fig. 10. Radiance distribution comparison (a) when the ND filter is normal to the LOS, and (b) when the ND filter is tilted by 2° to the LOS. The ghost cluster shifted by the ND filter appears as (1) and (2).
The ghost pattern is much more complex with the wedge scanner module, and the ghost radiance of the 2nd generation split is scattered irregularly. There are two distinctive ghost radiance clusters that appear when the ND filter is tilted by 2°. In Fig. 11(b), cluster (1) is formed by the reflection of the TCM wedge compensator and the SCM. The rays in cluster (2) are originally reflected from the rear surface of the bandpass filter, and the front surface of the ND filter [2]. Then they are reflected and refracted by the SCM. Although this cluster appears distinct from the FOV of the RCM, in the single instantaneous case, it still appears within the FOR of the system. The rays in this cluster have typical ray paths that disappear from the FPA when conventional forward ray tracing is performed, which uses the ray bundle of the corresponding incident angle with the RCM only. As shown in Fig. 10(b), the reverse ray tracing method is more intuitive to keep track of any altered ghost paths than the conventional ray tracing method, as the altered ghost irradiance always appear in the ray tracing result. However, a collective analysis is needed, which accumulates all separate cases constituting a single frame, for a better understanding of the behaviors of the rays.
Fig. 11. Accumulated radiance in front of the system: (a) the accumulated signal signifying the FOR of the system and (b) the ghost radiance, excluding the signal. (1) is the signal-shaped cluster near the FOR, (2) the FOR-shaped ghost cluster in FOR and (3) the circular ghost cluster surrounding FOR.
3.2 Accumulated ghost radiance regarding the FOR
Once the rays have been accumulated to form a single frame, the ghost radiance distribution pattern can be plotted in angular space. The FOR and ghost irradiance patterns, when ND3 is inserted, are shown in Fig. 11. The accumulated signal-forming FOR is shown in Fig. 11(a). As the signal rays are excluded, the three major ghost signatures rise, as shown in Fig. 11(b). Cluster (1) is a signal-shaped cluster near the FOR, cluster (2) is an FOR-shaped cluster in the FOR, and (3) is a circular cluster surrounding the FOR.
Cluster (2) is the primary ghost pattern that should be eliminated. To find the tilt angle of the ND filter, which can push these patterns away from the FOR, ray tracing is performed with the tilt angle increased from 1° to 6°, in increments of 1°, as shown in Fig. 12.
Fig. 12. Movement of the ghost radiance induced by the reflection from the ND filter according to the ND filter’s tilt angle: (a) 1°; (b) 2°; (c) 3°; (d) 4°; (e) 5°; and (f) 6°. (2) is the FOR-shaped ghost cluster and (4) is the ghost of the signal-shaped cluster near the FOR.
As shown in Fig. 12(a)–13d, the ghost pattern (2), within the FOR from Fig. 12(a), is gradually pushed away from its initial position as the ND filter’s tilt angle increases. Ghost pattern (4) from Fig. 12(b) has been split from the TCM wedge compensator, and reflected again from the ND filter’s front surface. This pattern is also pushed away according to the ND filter’s tilt angle. When the tilt angle reaches 5°, shown in Fig. 12(e), the major ghost cluster gradually fades. This cluster finally disappears when the tilt angle reaches 6°, shown in Fig. 12(f). Figure 13 shows the normalized radiance distribution of the major ghost cluster in Fig. 12, according to the ND filter’s tilt angle. The ghost radiance distribution is a vertical cross section, normalized by the maximum radiance of the signal.
Fig. 13. The accumulated ghost radiance as a function of the ND filter’s tilt angle. The distribution has been normalized by the maximum radiance of the signal.
As the tilt angle increases from 0° to 4°, the normalized maximum ghost radiance decreases from 0.2739 to 0.0218, and the peak of each ghost radiance distribution increases from −0.20° to 1.37°. When the tilt angle reaches 5°, the maximum ghost radiance drops to 0.0090 and the peak returns to −0.5°. When the tilt angle becomes 6°, the ghost irradiance pattern remains unchanged, with negligible radiance. This result shows that the ghost radiance, resulting from reflections from the ND filter, becomes negligible from the optical path when the tilt angle reaches 5°.
3.3 Minimizing the static ghost signal path by replacing the ND filter with a mechanical vignette
Figure 14 shows the ghost irradiance as a function of tilt angle of the ND filter, for each path. They are normalized by the total stray light radiance when the tilt angle of the ND filter is 0°.
Fig. 14. The ghost radiance as a function of tilt angle of the ND filter, normalized by the total ghost radiance when the ND filter’s tilt angle is 0°. The error bars signify the transmittance radiance error for each case of the ND filter’s tilt angle. The NDF indicates the front surface of the ND filter and the NDB indicates the back surface of the ND filter. The BPF indicates the front surface of the Bandpass Filter and the BPB indicates the back surface of the Bandpass filter. NDF-NDB indicates the reflection between NDF and NDB, and rest of the legends as such.
Figure 14 confirms that the ghost radiance reflected from the ND filter can be significantly reduced by tilting the ND filter by 5°. This Fig. also shows that the residual ghost radiance, such as the radiance induced by the reflection between the front and back surface of the ND filter and Bandpass filter, dominates when the tilt angle exceeds 5°.
After careful review of these results, and the mechanical design, we decided to replace the ND filter with a mechanical vignette. Although it is usual to place the mechanical vignette at the aperture or intermediate focal plane of the system, its function of reducing the transmitted flux were expected work in the nearly collimated region where the ND filter used to be. By eliminating the ND filter, the ghost radiance can be reduced to 23% of the radiance when the ND filter is mounted normal to the chief ray of the center field. The footprint of the full field rays, of the receiving optics module on the ND filter’s position, is shown in Fig. 15(b).
Fig. 15. (a) Schematic of the mechanical vignette plane position in the RCM. (b) Footprint of the field rays covering the FOV on the mechanical vignette surface.
The size of the footprint is 21.43 mm by 19.62 mm. The shape of the footprint is partially vignetted on the upper side, like the shape of the L1, which was cut to accommodate the TCM (cf. Figure 4). The design of the mechanical vignette was a wheel with simple circular holes, of varying diameters. This was to avoid possible interference or diffraction given that the active LADAR system utilizes a single wavelength fired from the LM. The comparison between accumulated radiance in front of the system with the ND filter and the mechanical vignette is shown in Fig. 16. It can be confirmed that the ghost signatures in Fig. 16(a), (1) through (3), were eliminated in Fig. 16(b).
Fig. 16. Accumulated radiance in front of the system: (a) result with the ND filter mounted 2° tilted to the optical axis. (1) is the ghost radiance from the TCM wedge compensator, (2) from the internal reflection of the ND filter (3) from the ND filter and SCM (b) result with the mechanical vignette.
Since the image data of the LADAR system is created as a point cloud, investigating a relative illumination is sufficient to evaluate the impact of the mechanical vignette on the optical performance. Figure 17(a) shows the normalized relative illumination from the center to the edge field, according to the hole radius. Figure 17(b) shows the normalized transmission ratio as a function of hole radius.
Fig. 17. (a) Relative illumination, normalized by the peak irradiance when the hole radius is 11 mm, and (b) the normalized transmission ratio as a function of hole radius.
The normalized relative illumination has a rather flat distribution, regardless of hole radius. Given that the footprint on the mechanical vignette plane is smaller than 22 mm in diameter, a radius of 11 mm is long enough to account for all aperture rays. Due to the vignette shape in Fig. 15(b), the transmittance converges when the radius reaches 9 mm. The normalized relative illumination ratio between the center and the edge field is from 0.97 to 1, with a standard deviation of 0.0154, according to the mechanical vignette hole radius. As shown in the results presented in Fig. 15 and Fig. 17, a simple hole-shaped mechanical vignette works as intended as presented in Section 3.3. Since the optical component was excluded, the optimum focal point was shifted by 153 µm. The spatial resolution is expected to be improved as the RMS spot size of the center field with the mechanical vignette was decreased from 21 µm to 14 µm.
In conclusion, it is possible to replace the ND filter wheel with an iris-like mechanical vignette, with minimal signal loss on the edge of the FOV, given that the ND filter is in the near-collimated region of the RCM’s optical path. Our mechanical vignette design is shown in Fig. 18. Note that the mechanical vignette has 8 slots, from total block to 100% transmittance, while the ND filter wheel has 5 such slots.
4. Field test result and discussion
A comparison between the acquired images is shown in Fig. 19.
Fig. 19. (a) Actual CCD image; (b) the accumulated LADAR image, demonstrating the ghost for ND filter 6, a 50% transmittance and a tilt angle of 1°; and (c) a LADAR 3D image acquired using the mechanical vignette with 50% transmittance. The color indicates the distance from the system front. The distance is from shorter when the pseudo color is red, and longer as the color becomes closer to the blue.
It is clear that the ghost signals have been significantly reduced in Fig. 19(c). The antennas on the top of the object are much clearer, so that at least five can be identified, and the handrail also now resolvable. The total number of points in Fig. 19(b) is 76,068, compared with 64,327 in Fig. 19(c). The ratio of the total number of points is 1:0.81, when each of the number of points is weighted to have 50% transmittance, as shown in Table 5.
Table 5. Comparison of the number of points in the LADAR image.
The stray light ratios, according to the ND filter’s tilt angle, are shown in Table 6. The stray light to signal ratio is 0.21 when the ND filter is tilted by 1°.
Table 6. Stray light ratio.
From calculations, the ghost radiance induced by ND filter 6 has a ratio about 0.19, given that the number of points ratio decreased to 0.81 when the ND filter was replaced, as shown in Table 5. The calculated stray light ratio of 0.21, from the stray light to signal ratio when the ND filter is tilted by 1° from Table 6, coincides well with this value, as shown in Table 7.
Table 7. Stray light ratio comparison.
To validate our backward ray tracing method, error analysis was performed in two ways. The first method used the accumulated irradiance pattern-forming FOR. The second method used the irradiance ratio of the signal, according to the ND filter’s transmittance. The error between the measured transmittance of the ND filter and the flux, calculated from the accumulated ray flux, is presented in Table 8 and Fig. 20. The calculated error reduces as the transmittance of the ND filter increases. The error between these two values is ≤3%.
Fig. 20. The error between the measured transmittance of the ND filter and the normalized signal flux, calculated by the accumulated flux.
Table 8. Flux error induced by the calculation method.
5. Conclusions
A new method was proposed to calculate the ghost path using backward ray tracing. Each path was categorized for every instantaneous sampled case and accumulated in angular space. The results of this method are intuitive given that the ghost radiance, when moved from the FOR, still appears outside the FOR region of the angular coordinate system. While such ghost radiance normally disappears from the FPA when traced using conventional ghost analysis method [4]. In other words, our novel reversed stray light analysis method is efficient and intuitive. It provides better understanding of the continuous behavior of ghost radiance, in relation to optical component orientations (cf. Figure 14). Whereas the conventional method is effective and direct when performed for stationary optical systems.
To eliminate the primary ghost path of the system, the ND filter was replaced with a stop-like mechanical vignette. As a result, the total number of points acquired for the same object decreases by 19%, with dramatic visual improvement. These two results also coincide with the ray path analysis showing the ND filter-related ghost irradiance is about 23% of the total irradiance incoming to the RCM. The improvement, from using the mechanical vignette, can also be identified visually, where the resolution of Fig. 19(c) is substantially better than that of Fig. 19(b), and it is without the ghost pattern shown in Fig. 2(b).
Figure 21 shows the 3D image of a traditional Korean architectural building near a beach. This image has been geo-referenced, so that signals from multiple images are aligned in a single 3D Cartesian space. When tilted from the angle at which the 3D image was acquired, the image shows a typical laser shadow. The resulting image shows no noticeable optical defects now that the ND filter has been replaced.
Fig. 21. Geo-referenced image example after the system improvement. The 3D image was taken at the same angle and is displayed tilted.
Our novel reverse ray tracing method has been confirmed as effective for evaluating a LADAR system with a Risley prism scanner, and with a complicated operation concept. The calculated radiance and flux results of the accumulated ray data has been compared to actual image data acquired in the field. A comparison shows that the method is well fitted to actual measurements. The proposed method is effective for stray light analysis of many other optical systems, with complicated scanning mechanisms such as the Risley prism.
Appendix
Acronyms
Funding
National Research Foundation of Korea (2017R1A5A1070354).
Acknowledgments
We acknowledge the support of Breault Research Organization through the user licenses for Advanced System Analysis Program (ASAP) for ray tracing computation.
Disclosures
The authors declare no conflicts of interests.
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