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由前述分析可知:AOTF后楔角会影响衍射光在空气中的出射角度,所以在可见光范围内可利用合理的后楔角产生色散对声光作用的带宽内色散进行补偿,从而抑制光谱图像的退化,但现有的AOTF后楔角普遍被设计为补偿AOTF的横向色差以减少不同波段光谱图像之间的漂移。为了评估不同后楔角下AOTF器件的像质,文中以超声切角为6.5°的AOTF器件为例,根据前述理论方法计算出不同后楔角下的MTF。该AOTF波段范围400~1000 nm,光谱带宽2~10 nm,分为两个换能器通道,AOTF切型与声光互作用长度与前述示例一致。文中将不同后楔角的AOTF像质进行横向比较,后楔角范围为−8°~8°,其中−4.8°为针对该AOTF横向色差抑制所优化的最优角度。同时,文中分别计算了两个驱动频率下AOTF的MTF,99.4 MHz对应的声光互作用长度为2.6 mm,59.6 MHz对应的声光互作用长度为9 mm。MTF计算与线扩散函数相关,而线扩散函数的计算过程中会有系统等效焦距的影响,文中以50 mm等效焦距为例。
由图5可知,无论是短波还是长波,随着后楔角增加,AOTF的MTF随之增大,但是从截止频率的变化范围来看,改变后楔角对短波的影响更大。为了表征不同后楔角下AOTF像质优劣,文中采用MTF30作为量化指标,该指标取MTF等于30%处的空间频率作为评价像质的标准,30% MTF处的空间频率越高代表像质越好。文中计算不同波段、不同后楔角对应的MTF30如表1所示。
Figure 5. (a) MTF of 59.6 MHz (central wavelength 750 nm) with different rear cut angles; (b) MTF of 99.4 MHz (central wavelength 500 nm) with different rear cut angles
99.4 MHz 59.6 MHz Rear cut angle/(°) Spatial frequency/cycles·mm−1 @MTF30 Rear cut angle/(°) Spatial frequency/cycles·mm−1 @ MTF30 8 75.9 8 55.7 6 45.6 6 50.9 4 32.6 4 47.1 2 25.6 2 43.4 0 21.0 0 40.2 −2 17.7 −2 37.4 −4 15.3 −4 34.7 −4.8 14.5 −4.8 33.7 −6 11.7 −6 32.2 −8 7.2 −8 29.9 Table 1. MTF30 with different rear cut angles at 99.4 MHz (center wavelength 500 nm) and 59.6 MHz (center wavelength 750 nm)
在实际应用中,一般对成像系统的奈奎斯特频率处MTF更为关注,例如当应用要求奈奎斯特频率处MTF优于30%时,则可以通过查找表中的空间频率推导出满足应用需求的AOTF后楔角角度。同时,通过分析发现在现有AOTF −4.8°后楔角下的MTF30比0°后楔角的更低。所以,横向色差校正与更优的空间响应本身是一对矛盾,无法同时满足。当横向色差得到校正,则MTF会下降。如果针对MTF来优化后楔角,则横向色差会引起不同波长的光谱图像漂移。所以,设计阶段的MTF定量计算十分重要,可用以保证AOTF的后楔角设计能满足实际应用需求。
Influence of the AOTF rear cut angle on spectral image quality
doi: 10.3788/IRLA20210590
- Received Date: 2021-08-20
- Rev Recd Date: 2021-09-16
- Available Online: 2022-08-13
- Publish Date: 2022-08-05
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Key words:
- acousto-optic tunable filter /
- rear cut angle /
- spectral imaging
Abstract: Spectral image degradation is a common problem of acousto-optic tunable filter (AOTF) imaging spectrometers, and it is difficult to quantitatively predict. To quantitatively evaluate the image quality of spectral images, a modulation transfer function (MTF) calculation method including the influence of the AOTF rear cut angle is proposed. In this method, the line spread function (LSF) of the AOTF device is obtained by establishing the spectrum-space dimension response model of the AOTF, and then the theoretical MTF is obtained by Fourier transform of the line spread function. In the validation experiment, the deviation between the measured MTF value and the theory is less than 15% within the cut-off frequency. It is a theoretical basis for image quality evaluation of the AOTF. Furthermore, the influence of different AOTF rear cut angles on spectral image quality is discussed by this quantitative method. After simulation, it is concluded that the rear cut angle of the AOTF has difficulty meeting the requirements of lateral chromatic aberration and image sharpness at the same time. The cut angle needs to be selected according to the requirements of practical application. Therefore, it is significant to evaluate the image quality of AOTFs with different rear cut angles. The method is an important theoretical basis for AOTF device design.