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某水下大视场连续变焦光学系统选用0.48~0.64 μm可见谱段高灵敏度CMOS成像传感器,像元尺寸为2 μm×2 μm,像元数为3840×2160。经任务分解,具体设计指标如表1所示。
表 1 设计指标
Table 1. Design requirements
Parameter Value Work wavelength/μm 0.48-0.64 F-number 2.8-32 Diagonal field of view (DFOV)/(°) 62-5.9 Underwater distortion ≤5% Focus range 0.5 m-inf Working depth/m 11 000 Size (Without window)/mm2 ≤φ60(D)×220(L) Weight/kg ≤1.5 -
针对上述指标,下面讨论水下光学系统设计中的若干问题和设计方法。有关水下介质特性的报道已较多,此处不再赘述[16-19]。
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如图1所示,球罩和平板是两种典型的水下光窗形式。对于前者,球面与水介质形成负透镜,当光窗球心与镜头入瞳中心重合时,可消除相对畸变和倍率色差,但对于光阑后置的一次成像变焦系统,入瞳位置会随焦距的变化发生前后移动,当变倍比较大时,入瞳移动量大,像差变化剧烈,导致设计困难。另外,水的折射率还随着温度、盐度、水深等的变化发生变化,这些都对球形光窗变焦光学系统的设计造成困难[20-22]。
而平板光窗为无焦元件,除由光窗两侧折射率不同导致光学系统视场变小和成像倍率色差及相对畸变增大外,位于光窗内侧的光学系统像差特性基本不受外界水折射率变化的影响,这也极大地便利了大变倍比水下大视场变焦光学系统的设计,为文中水下大视场变焦光学系统优选的光窗形式[21-23]。
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水下平板窗口会影响入射成像光线的出射角度,进而减小后组物镜的有效成像视场[21-23]。
如图 2所示,由物方至像方依次设置水、平板光窗、空气、成像物镜和焦面。若设水介质的折射率为n1,光线进入窗口的入射角为
${\theta }_{\rm{in}}$ ,窗口材料折射率为n2,光线从窗口进入空气的出射角为${\theta }_{\rm{out}}$ ,空气折射率为n3,则有$$ {{n}}_{1}{\rm sin}{\theta }_{{\rm{in}}}={n_3}\rm sin{\theta }_{out} $$ (1) 若取水介质的折射率n1=1.33,空气折射率n3=1.0,可知,水下平板光窗会将成像物镜的有效视场缩小为空气中的约2/3。
进一步,设成像物镜在空气中的焦距为
${f}_{\rm{obj-air}}^{\rm{'}}$ ,在水下的等效焦距为${f}_{\rm{obj-uw}}^{\rm{'}}$ ,则有$$ {f}_{{\rm{obj-uw}}}^{\rm{'}}={n}_{1}· {f}_{{\rm{obj-air}}}^{\rm{'}} $$ (2) 若定义相对畸变
$$ Dist=\frac{{y}^{\rm{'}}-y}{y} $$ (3) 其中,理想像高
$y={f}_{{\rm{obj-uw}}}^{\rm{'}} {\rm{tan}}{\theta }_{{\rm{in}}}$ ,真实像高${y}^{\rm{'}}={f}_{{\rm{obj-air}}}^{\rm{'}} {\rm{tan}}{\theta }_{{\rm{out}}}$ ,整理可得$$ Dist=\dfrac{{\rm{tan}}\left(\mathit{{\rm{arcsin}}}\left(\dfrac{{n}_{1}{\rm{sin}}{\theta }_{{\rm{in}}}}{{n}_{3}}\right)\right)}{{n}_{1}{\rm{tan}}{\theta }_{{\rm{in}}}}-1 $$ (4) 此时,由平板光窗引入的相对畸变分布如图2所示,主要为正畸变(枕形畸变)。
此外,若设水对F线和C线波长光的折射率分别为
${{n}}_{\rm{1F}}$ 和${{n}}_{\rm{1C}}$ ,并取盐度0、温度20 ℃、浅水条件的水下工作环境,则有出射角差值${\theta }_{{\rm{outF}}}-{\theta }_{{\rm{outC}}}$ 随入射角的变化如图3所示,即知由平板光窗引入的倍率色差为正。图 3
${\theta }_{\rm{outF}}-{\theta }_{\rm{outC}}$ 随入射角变化分布示意图Figure 3. Schematic diagram of the change of
${\theta }_{\rm{outF}}-{\theta }_{\rm{outC}}$ vs angle of incidence为应对由水下平板光窗导致的上述问题:指标分解上,在设计阶段尤其要注意平板光窗对水下光学系统的视场压缩;光焦度分配上,物镜组总光焦度应为负,以校正平板光窗引入的正畸变;材料选择上,物镜组也应以高折射率高色散材料为主;而且,通过采用折射率相近、色散相差较大的材料组合可实现消色差平板光窗[23-25]。
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水下工况对光学系统有严格的包络限制,尤其是深海应用,光学系统包络直接影响耐压壳体与整机的体积和质量。针对表1中的技术要求,结合项目组设计经验[26],如图4所示,给出了一种三组联动变焦光学系统设计模型示意图。整个光学系统在PNNP型结构的后固定组中,引入像差稳定镜组,共包含:前固定镜组F、变倍镜组Z、补偿镜组C、中间固定镜组MF、像差稳定镜组AS和后固定镜组BF。其中Z和C组承担光学系统主要变倍能力,AS镜组对由Z和C组运动导致的动态像差做进一步稳定和补偿。提高了整个光学系统的像差校正能力,可进一步压缩长度,改善光学系统性能。
图 4 一种三组元联动变焦镜头设计模型示意图
Figure 4. Schematics of the design model of zoom lens with three linkage group
需要特别指出的是,该类三组元连续变焦设计模型兼具PNNP型无换根点的优点,在变焦方程及参数求解方面也可参考典型PNNP型变焦系统。设计过程中,只需单独控制像差稳定镜组的放大倍率不通过或平滑通过m=−1点,即可保证该镜组变焦过程平滑、连续、稳定,进一步简化了光学设计过程[27-30]。
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受工作环境限制,大多数水下成像光学系统需具备近距成像能力;对于变焦光学系统,还要求对同一近景目标,变焦全程图像应连续一致保持清晰;而对于电视摄影用途,对不同物距场景,对焦过程还应精准可控,以最大程度保证跟焦准确。此时,采用传统的整组或后调焦的方式均很难实现上述功能。
针对上述问题,在靠近物方侧的镜组中设置一组或几组镜片实现对近景目标的高效调焦和对不同物距目标的精准跟焦,并可同时保证变焦全程对近景目标的清晰成像。另外,调焦过程引入的呼吸效应视不同用途也应得到关注[27-29]。
Design of underwater large field of view zoom optical system
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摘要: 针对现有水下光学系统中存在的主要不足,就某大视场水下连续变焦光系统指标要求,从水下光窗选型、光窗畸变、色差等的影响入手,分析了水下平板光窗引入的相对畸变和倍率色差特性,给出了相应的应对措施。结合水下工况对包络和工作距的要求,给出了一种三组联动的变焦系统设计模型和相应调跟焦组件的设计方法;通过在PNNP型结构中引入像差稳定镜组,对动态像差做稳定和补偿,改善了光学结构的像差校正能力,同时规避了凸轮曲线断点问题;通过在物方侧镜组中设置调跟焦镜组,保证了变焦全程对近景目标的清晰成像。完成了一个4 K水下大视场连续变焦光学系统设计,该系统工作距为0.5 m~inf,设计波段为0.48~0.64 μm,采用3840×2160高灵敏CMOS面阵探测器,像元大小为2 μm,变焦全程F数最大恒定为2.8,可实现全视场5.9°~62°、10倍以上连续变焦功能,具有较短的变焦行程、平滑的变焦轨迹、优良的成像性能等优点。Abstract: Under the requirements of an underwater large field of view zoom optical system, the selection of optical window and its influence on objective lens were discussed, by which the relative distortion and lateral color induced by the plane window were analyzed and corresponding design methods were given. Regarding the special envelope and working distance requirements of the underwater optical system, a three-part zoom system design model and the design method of the corresponding focusing components were provided by introducing aberration stabilizers in the PNNP structure, dynamic aberration correction capability of the optical structure was improved, also, the problems of the cam curve breakpoints were avoided; by setting the focus lens group in the objective parts, close-range imaging through the entire zoom range was guaranteed. A 4 K underwater large field of view zoom optical system was completed using 3840×2160 high-sensitivity CMOS detector, with 0.5 m-inf working distance, 0.48−0.64 μm work waveband, constant F number of up to 2.8 and 5.9°−62° full field of view. The image quality and tolerance characters are validated by an assembled lens and its underwater imaging experiments.
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Key words:
- ocean optics /
- underwater optics /
- zoom lens /
- large zoom ratio /
- optical design
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表 1 设计指标
Table 1. Design requirements
Parameter Value Work wavelength/μm 0.48-0.64 F-number 2.8-32 Diagonal field of view (DFOV)/(°) 62-5.9 Underwater distortion ≤5% Focus range 0.5 m-inf Working depth/m 11 000 Size (Without window)/mm2 ≤φ60(D)×220(L) Weight/kg ≤1.5 -
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