A new stray light analysis method and some suppression principles of panoramic annular lens (PAL) are introduced in this paper. The proposed method is to find stray light paths which are caused by ray splitting on two refractive surfaces of the PAL block and then cut them off. Following this principle, the stray light paths can be eliminated in the design progress by adding specific merit functions into the optical software. The methods to reduce scatter, diffraction and other stray light are also proposed. A new PAL with a field of view (FOV) of 30°~100° × 360° is designed. The stray light is suppressed more than 80% compared with a similar conventional PAL. The stray light path analysis method also can be used in other catadioptric optics.
©2013 Optical Society of America
Panoramic optical system like panoramic annular lens (PAL), fisheye lens and catadioptric system has a wide field of view (FOV), even over 180°. It’s extensively used in the surveillance system, navigation system and robotic vision system, etc [1, 2]. The advantages of PAL include the compact size, small f-θ distortion and simple manufacture structure. However, because it contains two reflective surfaces, light paths in its block are complicated compared with the purely refractive optics. In the usage of PAL it’s found that if a highlight source appears in the FOV, like the sun or a lamp, the image will be covered by serious stray light. In the refractive optics, stray light mostly comes from the multi-reflections between lenses, scatter from the internal lens tube or abnormal paths caused by not well-baffled. The majority of stray light suppression methods including the usage of the lens hood in long focal lens or the special baffle structure in wild-angle lens [3, 4]. Shifting the aperture stop to the detector side as close as possible is also a traditional approach .
The publications to explain the stray light source in PAL are few up to the present. V. N. Martynov reported two possible stray light paths in this optics . One path is from the incident ray that passes though the aperture directly without any intersections on the reflective surfaces. The other is from the incident ray that passes through the aperture stop after several reflections between the block’s reflective or refractive surfaces. But the solution to solve the problem had not been put forward in detail. Tadashi Doi submitted a patent about the probable stray light paths and some simple methods . In the patent, the stray light was thought to be generated from the reflections in the block once, twice or three times, and the solutions included digging holes, dull polishing and slotting to cut off the stray light paths. But the performance can’t be evaluated since no detailed implementations were given. These methods are only some alternative ways to produce small and rough plastic PAL blocks by stamper on a large scale, but can’t produce large PAL blocks with a high degree of accuracy.
PAL system is different from most of the wide angle systems since it has two reflective surfaces. Except for the common stray light paths in the refractive optics, some non-imaging rays have the ability to reach the detector after some reflections in its block. Compared with the catadioptric system, the lens hood can’t be used in the PAL system. Any obstacles will image on the detector since its first refractive surface is a field stop. But this surface is an aperture stop in the catadioptric system, so it doesn’t affect the image obviously if the surface is partly blocked. The previous PAL stray light experiments show that the image becomes obscure when a strong light source appears near the optical axis or the edge of the ring-shape reflective surface. So this area should be taken into notice that it maybe the entrance of stray light in PAL.
In this paper, a novel stray light analysis method and some suppression principles of PAL system are proposed. Stray light is distinguished into five kinds: light passing though the aperture stop without any reflective surfaces, light being reflected several times between the refractive surfaces, light being scattered by the reflective surfaces, light being diffracted at the edge of the aperture stop and the edge of the front reflective surface. The second kind is thought to be the largest stray light source, so it’s analyzed in detail and some suppression principles are given. In the implementation, one prototype that has the ability to suppress stray light mentioned above is designed by adding specific merit functions into the optimization progress. The FOV is 30°~100° × 360°, F# is 2.8 and focal length is −5.5mm. The MTF is higher than 0.7 at 100lp/mm in all FOV. The stray light suppression performance is shown by stray light ratio comparison with a similar conventional PAL system using non-sequential optical simulation software. The new PAL shows better performance in stray light suppression than the conventional one.
2. The kinds of stray light generated in PAL system
The stray light in PAL system is possibly caused by multi-reflections, scatter or diffraction, etc. which is generated from coating defects, material’s BSDF character or abnormal light paths. Some of them can be suppressed by optical design while others can only be alleviated by advanced material technology. The optimal method is to cut the stray ray paths in the PAL block, but not to block it after entering the aperture stop. The stray light caused by the splitting on the refractive surfaces and then reaches the detector after several reflections can be removed by optical design. An evaluation method and some suppression principles are discussed in detail.
2.1 Stray light entering the stop by multi-reflections or without any reflective surfaces
The stray light paths of these kinds are shown below. In Fig. 1(a), the red and blue lines are the imaging and the stray ray paths respectively. The stray rays reach the detector without any reflections. In Fig. 1(b), blue rays reach the detector after several reflections between surface 3 and 2. Both kinds of theses stray rays aren’t related to ray splitting. If the stop aperture is set at a proper position, they won’t reach the detector. Most of the PAL system’s apertures stop are set at the edge of surface 4 or the edge of the following lens’s front surface, so that any critical surfaces can’t be seen before the aperture stop . This kind of stray light can be easily eliminated.
2.2 Stray light reflected several times between two refractive surfaces
The stray light paths of these kinds are shown below. In Fig. 2(a), after the stray rays entering surface 1 and being reflected by surface 2, they are not be reflected to surface 3 as the imaging rays. Some of them reach surface 1 and split. Due to the Fresnel reflection law, any light traversing from glass to air will be split into refraction part and reflection part. The former part leaves the block while latter part is reflected back to surface 4. After passing through surface 4 and the relay lens, some of the splitting rays reach the detector. In Fig. 2(b), the imaging rays split on surface 4, the refractive part (red rays) reaches the detector at the correct position while others (blue rays) are reflected again between surfaces 3 and 4. Some of them reach the detector. The rays will be reflected several times between surfaces 3 and 4 if the energy of the reflected part is strong and splits several times. In that condition, a series of speckles appear on the detector. They will cover the detector and make the image hard to be distinguished from the noise.
2.3 Stray light scattered by the reflective surfaces
The scatter stray light is generated on all the optical surfaces and mechanical parts, even after being coated or polished. In Fig. 3(a), stray light is generated by scattering on surface 3 and relay lens. In Fig. 3(b), stray light is scattering on the lens tube. This kind of stray light can’t be suppressed completely but can be alleviated by advanced coating technology.
2.4 Stray light diffracted by the aperture stop and reflective surface’s edge
The diffraction stray light in PAL system is generated at the aperture stop and the edge of the front reflective surface. In Fig. 4(a), diffraction light is generated at the edge of aperture stop (surface 4). In Fig. 4(b), diffraction light is generated at the edge of surface 3. This kind of stray light is also hard to be totally suppressed but partly be removed.
2.5 Other stray light in relay lenses
Since the PAL system’s stop is set before the relay lens, other kinds of stray light in relay lens can be analyzed apart from the stray light which is generated in PAL block. Like other refractive optics, the stray light comes from multi-reflections between lenses and the inner wall of mechanical tube. It has to come into notice that the stray light between its block and relay lens should be suppressed to the best to prevent them from entering relay lens.
3. Principles of stray light suppression
Since the stray light in section 2.2 come from the defect of optical design, and it can be mostly avoided in the optimization process, two mathematical models are established and some optimization principles are proposed below to cut off the stray ray paths in theory.
3.1 The stray light generated by the reflections on surface 1 and the suppression principle
Two imaging paths starting from A0 and B0 in a typical PAL block is shown in Fig. 5. The black bold and thin lines respect the reflective and refractive surfaces respectively. Surface 4 is set as the aperture stop. The path of a high FOV ray starting from A0 (pink hard line) hits the block at A1, A2 and A3 in sequence, leaves the block at A4 from surface 4. The path of a low FOV ray starting from B0 (blue hard line) hits the block at B1, B2, and B3 in sequence, leaves the block at B4. B1B2 and B1C2 (black dash line) are symmetrical about N (the normal at B1). If a virtual ray from C2 is traced, the intersection of C2C1 on the block (C1) can be obtained. And if C1 is on surface 1, one ray from C0 can be refracted into the block though C1, reflected by surface 2 at C2, and then arrived on surface 1 at B1. Some splitting rays leave the block to the air while others are reflected back to the block. The latter part hits the block at B2 and B3, leaves the block at B4. The reflected ray’s path overlaps the imaging ray path from B0. So this is a stray ray path, which starts from C0, hits the surface at C1, C2, B1, B2, B3 and B4 in sequence. If the stray light energy from C0 is strong while the imaging energy from B0 is weak, the image of B0 will be covered by the strong stray light from C0, which make B0 difficult to be distinguished on the detector.
The way to suppress this kind of stray light from C0 is by absorbing it at C2, so the stray ray path C2B1 can be cut off on surface 2. To avoid the imaging rays from low FOV being absorbed, all the distance from C2 to the optical axis (SagC2) should be longer than all the distance from A2 to the optical axis (SagA2). In all imaging rays' intersections on surface 2, the sag of A2 formed by the highest FOV's marginal ray is the longest (SagA2max). While in all the symmetrical virtual rays' intersections with surface 2, the sag of C2 formed by the lowest FOV's marginal ray is the shortest (SagC2min). So if SagC2min is larger than SagA2max, and the ring range from C2min to the edge of surface 2 is dulled polished and black coated, all the stray light paths from C0 are cut off.
In Fig. 6, the PAL block is set upwards and a coordinate system is established at the central of the system’s aperture stop. A is the chief ray vector from P0 with an incident angle of θ. It hits surface 1 at P1(x1,z1). The normal vetor at this point is N1. The refractive vetor B starts from this point and hits surface 2 at P2(x2,z2). If A is the chief ray, it will pass through O after being reflected by surfaces 2 and 3. Vector B’ and B are symmetrical about N1. B’ hits surface 2 at P’2(x’2,z’2). If all the surfaces forming the PAL block are spherical, they should satisfy the equations as:
The coordinate of P1(x1,z1) can be solved with Eq. (1) and the incident vector A from P0. Since N1 is the normalized gradient of fs1(x, z) at P1, the refractive vector B can be expressed as nB = A + p•N1 by the refraction law. n is the refractive index of PAL block. The symmetrical vector of B’ can be calculated by B’ = -B + 2 N1 (N1•B) by the reflection law. The coordinates P2(x2, z2) and P2’ (x2’, z2’) on surface 2 can be solved by Eq. (2) with B and B’. If A is the ray from the lowest FOV, the coordinate of P2’ can be written as P’2min(x’2min, z’2min). Tracing the ray from the highest FOV on the other side, P1max (x1max, z1max) and P2max (x2max, z2max) can be determined too. It has been discussed above that the horizontal distance between P2max (x2max, z2max) and P’2min(x’2min, z’2min) is closest. Therefore, if the difference of two absolute x values meets Eq. (4), this kind of stray light can be avoided.
3.2 The stray light generated by the reflections on surface 4 and the suppression principle
Two imaging paths and one stray light path are drawn in hard lines and dash lines respectively in Fig. 7. The structure is the same as in Fig. 5. Two rays starting from A0 (pink hard line) and B0 (blue hard line) hit the surfaces at A1 (B1), A2 (B2) and A3 (B3) in sequence, and leaves the block from A4 (B4) on surface 4. N is the normal at B4. The imaging ray B3B4 splits at B4 into a refractive ray and a reflective ray. The former ray reaches the detector, and the latter ray is reflected back to the block by surface 4. After it’s reflected again between surfaces 2 and 3 at B5, B6 and B7, it leaves the block from B8 (blue dash line). It is possible to pass through the relay lens and reach the detector. So it’s a stray light path which starts from B4, hits the surfaces at B5, B6, B7, and B8 in sequence. If the imaging energy from B0 is very strong, the splitting stray light at B4 will be reflected between surface 2 and 3 (or 4) and splitting several times, which results in a series of glare spots on the detector.
The way to suppress this kind of stray light (B7B8) is by pushing the intersection B8 down to the edge of surface 4 (O1) in the optimization progress, and making the reflections between surface 2 and 3 as much as possible. Since in PAL system almost of the surface 3 is concave while all the surface 2 is convex, the more times the ray is reflected, the farther the intersection is away from surface 4. In all the sag of B6 (SagB6), the ray from the lowest FOV is longest. So if this intersection is below O1, other FOV’s B6 are all below O1. In fact, the path in the block is very complex, reflections are happened not only between surfaces 3 and 2, but also with surface 1, so a part of stray rays still can reach surface 4 after several reflections. However, the energy is weak and most of them will be absorbed by the inner wall of the mechanical tube when they pass though the relay lens. This kind of stray light is different from the kind in section 3.1. Firstly, the former kind is non-imaging energy before entering the block, but the latter kind is imaging energy when it enters. Some of it splits and becomes stray light after several reflections. Secondly, this kind of stray light can’t be totally suppressed like the former kind.
The mathematical model of the PAL block in Fig. 8 is the same as in Fig. 7. A vector from P0 hits surface 1, 2, 3 and 4 at P1, P2, P3 and P4, which are named as A, B, C and D respectively. D and E are symmetrical about the Z axis. P5 is the intersection of E on surface 3. F is the reflective vector of E and has an intersection P6 on surface 2. O1 and O2 are two edges of surface 4. Like the analytical method before, the coordinate P5 (x5, z6) and P6 (x6, z6) can be calculated by ray tracing from vector E. It has been discussed above that the x value of P6 from the lowest FOV is the largest. So if this x value of P6 (x6min, z6min) is smaller than the x value of the O1 (-xO, zO), all the x values of other FOV are smaller than -xO. But in the optimization progress, the diameter of PAL block becomes too large when the P6 is squeezed to O1. So a compromise must be made between the PAL block’s diameter and the stray light suppression performance in this kind of stray light. The Fmin(x) should be optimized to the minimum at an acceptable diameter. It’s shown in Eq. (5).
3.3 The scatter, diffraction and other stray light in PAL system
The scatter stray light is generated on any optical surfaces, no matter the surfaces are coated or not. It’s related to coating defect and surface BSDF character, etc. It can’t be completely eliminated in PAL system by optical design, but it can be suppressed much by reducing the area of the reflective surfaces, coating the useless surfaces black and increasing the PAL block’s axial length which made stray light passing though the stop harder.
The diffraction stray light is generated at the edge of aperture stop in all optics. One way to suppress it is by adding a Lyot stop at the exit pupil . Since the PAL system has a front mirror, diffraction is also generated at its edge. It’s necessary to add another Lyot stop at the image of surface 3 which is imaged by other refractive surfaces.
Because the stop is located between the PAL block and the relay lens, the stray light generated by the relay lenses can be analyzed separately. It can be suppressed like common refractive optics, so it’s not the emphasis in this paper. But it must be taken into notice that the stray light between the relay lens and PAL block is complicated. To avoid it from traveling thought the relay lens, some ring-shape baffle vanes should be added between them.
In the implementation, a full frame monochrome sensor was chosen as the detector. The resolution of the camera is 4872 × 3248, with a pixel size of 7.4μm. The PAL system’s spectral range is 0.486μm~0.656μm. The FOV is 30°~100° × 360°. The F# is about 2.8 and focal length is about −5.5mm. The initial structure of the block is composed of three cemented glass, which is favorable for achromatic PAL [9, 10].
4.1 The optical design and performance of a new PAL and a conventional PAL
The structure and MTF of a new PAL that can suppress stray light is shown in Fig. 9(a). Constrains that can cut off the stray light paths mentioned in section 3 are added to the merit functions during the optimization progress. The stray light analyzed in section 3 is suppressed to the best. The PAL block materials are BAK9, ZF52 and QF10 (Chinese glass catalog). The length is about 188mm, the largest diameter is about Φ160mm, and all the surfaces are spherical. The MTF is higher than 0.7 at 100lp/mm in all FOV. The aperture stop is set at the front surface of the first relay lens. For the sake of the stray light suppression performance contrast, another conventional PAL is designed in Fig. 9(b). The initial structure of this one is as same as the new one before being optimized. The only difference is the stray light suppression constrains are not included in its merit functions during the optimization progress. Other parameters like the amount of lenses, glass material, focal length, wavelengths, F#, FOV and distortion are almost the same. The image quality is similar too from the MTF.
4.2 The stray light analysis of two PAL systems after non-sequential optical simulation
Two system profiles are shown in Fig. 10. The relay lens is surrounded by mechanical tubes. The cyan crosshatching profile is a tube which has inner ring-shape baffle vanes. The edge of the baffle is close to the envelope of the rays. The green crosshatching profile is a normal lens tube. The blue surfaces 1 and 4 are non-absolutely refractive surfaces. The yellow edges are absorptive surfaces. The pink surfaces 2 and 3 are reflective surfaces. Two systems don’t contain Lyot stops since the images of surface 3 are not real, and the exit pupils are both behind the detectors. But the Lyot stops should be considered in other PAL systems.
It’s considered that most of the stray light is generated by the reflections on the blue refractive surfaces. So in the first simulation, the reflection coefficient of these surfaces is designated as 2%, other surfaces are absolutely transparent or absorptive. All the stray light sources like scatter or diffraction are ignored. In the second simulation, all the surface defects may have the possibility to generate stray light mentioned in section 2 are added. The scatter model of surfaces 2 and 3 fits Harvey model . The scatter model of the yellow part and inner wall of the mechanical tubes fits Lambertian model. The simulation light source is a point source, whose energy distribution is Lambertian. In the simulations, the source is located from the optical axis to the edge of surface 1, shown in Fig. 10. The source's distance to surface 1 is constant. The main emitting direction is always perpendicular to surface 1.
The result of stray light suppression performance is shown in the chart of Fig. 11 from the results of non-sequential optical simulation. The abscissa axis represents the radius from center of the detector in millimeter. The interval is 0.1mm from 5.8mm to 7.6mm, and 1mm from 7.6mm to 24.6mm. The designed imaging area is from 6.5mm~21.6mm (yellow area). The ordinate axis represents the ratio of stray light energy vs. the total energy at the same radius. The hard and blue lines respect the result after the first and second simulations. The blue and red lines respect the new and the conventional PAL.
The hard lines are obtained after the first simulation. The new PAL’s stray light ratio is only 0.001% at all positions (hard blue line). The conventional PAL’s stray light ratio is 100% below 6.0mm. It comes from the splitting rays on surface 4 and arrives on the blind area of the detector. This kind of stray light is analyzed in section 3.2 which is generated from the splitting rays on surface 4. From 6.0mm~6.6mm, the ratio drop to 0.0012% rapidly. From 6.6mm~13.0mm, the ratio is about 0.0015%, which is almost the same as the new one. From 13.0mm~21.6mm, the ratio suddenly jumps to 0.039% on average. This kind of stray light is analyzed in section 3.2 which is generated from the splitting rays on surface 1. Since it’s on the edges of the detector, it damages the images from high FOV, which is observed in the early PAL experiments. The comparison of the two hard lines proves that two kinds of stray light analyzed in section 3 are extremely suppressed in the new PAL. The stray light performance is much better than the conventional PAL, especially in high FOV.
The dash lines are obtained after the second simulation. It can be seen that the stray light ratio in both systems are increased. Especially from 6.0mm~6.3mm of the new PAL, it is much higher than the ratio at the same location in the first simulation. It’s because some scatter light from the low FOV arrives on the detector while the imaging light is mostly stopped by surface 3. However, this part of stray light is in the blind area, so it doesn’t affect the image quality. Except this part, both system’s ratio trendies are almost the same compared with the first simulation, only a little higher. So the other kinds of stray light are not dominating factors in the PAL system.
From the above simulations, It can be seen that the scatter and diffraction light (sections 2.3~2.5) are not the dominated stray light sources in PAL system. And these kinds of stray light distribution are uniform on the detector. Most of the stray light comes from the splitting rays on surfaces 1 and 4 (section 2.2). It’s a special kind of stray light in PAL or catadioptric systems which have reflective and refractive surfaces. It doesn’t come from the coating defects but from the system’s optical structure. By adding stray light suppression merit functions into the optical optimization progress which discussed in section 3, this kind of stray light can be mostly eliminated.
The new way to suppress stray light in PAL system can be also used in catadioptric systems. Firstly, tracing an arbitrary imaging ray’s symmetrical virtual ray on the refractive surfaces, if it can leave the system af`ter several reflections or refractions, this ray path must be a stray ray path. Secondly, adding special stray light suppression merit functions into the optical software. After the optimization, the stray ray path will be cut by absorbing surfaces or leave the system.
In this paper, a novel stray light analysis method and some new stray light suppression principles of PAL are proposed. The stray light generated by the reflections on refractive surfaces in PAL block is proved to be the strongest stray light source. The diffraction and scatter stray light takes up a small amount. By adding stray light stray light suppression merit functions into optical software, a new PAL that can suppress stray light is designed. Compared with a similar conventional PAL designed without these functions, the non-sequential simulation results show the stray light suppression performance of the new one is much better than the conventional one, and the stray light ratio is nearly 80% lower. The analytical method and suppression principles can also be used in other catadioptric systems which have reflective and refractive surfaces.
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