用于景深延拓的非旋转对称相位板特性研究与新的设计
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摘要
众所周知,任何成像系统都具有一定的景深,而与之所对应的概念在像空间中则被称为焦深。只有景深范围之内的物体才能够被清晰成像,而超出景深范围的物体经光学系统所形成的图像将会变得模糊,从而引起细节、纹理的丢失。减小系统的相对孔径可以在一定程度上达到扩展景深的目的,但是这样做的代价却是系统分辨率的降低。1995年,美国科罗拉多大学的E.R.Dowski博士等人提出了一种波前编码成像技术,非常好地解决了传统成像系统在扩展景深时所遇到的困境。通过在孔径平面上引入一个合适的相位掩模板,成像系统的传递函数就会对离焦参量以及引起离焦的因素,如外界温度变化、系统机械结构不稳定等变得非常不敏感,从而使系统景深得到了极大的扩展。
波前编码成像技术主要由光学设计以及数字图像复原两个方面组成。性能优良的相位掩模板加上强大的复原算法是波前编码成像系统获得惊人效果的关键所在。这项技术发展至今,可以用于景深延拓的相位板层出不穷,且可以分为旋转对称型和非旋转对称型两大类。由于非旋转对称型相位板具有更加优秀的景深扩展能力,所以这类相位板成为了研究的重点和热点,而本文也正是以非旋转对称型相位板为核心来开展相应的研究工作的。
本文的主要工作可以概括为以下四个方面,而其中所使用的方法以及得到的结果就是文章创新性的直接体现。
第一,首次在统一框架下对主流非旋转对称型相位板在景深扩展能力、对初级像差的敏感性、点扩散函数中心偏移效应、中间图像的可恢复性以及加工难度五个方面进行了数值分析,并且以大量翔实的数据为基础建立了波前编码成像系统的性能评价体系原型。尤其值得一提的是,在已有的研究文献中,几乎鲜有加工精度对相位板性能所带来影响的讨论,而本文的工作很好地弥补这个不足。
第二,提出了一种基于多项式面型拟合的方法,可以用来简化波前编码成像系统所对应的离焦传递函数解析表达式的计算,而这对于不适用由E.R.Dowski博士所提出的经典计算方法的相位板而言正好是一种有益的补充。
第三,在充分考察已有相位板特性以及面型特点的基础上,本文提出了几种包括改进的对数型相位板、中心相位补偿型相位板以及叠加正弦分量型相位板在内的新的相位板,并且从理论和实验上证明它们也具有良好的景深扩展能力。此外,本文还首次对文献中鲜有提及的三角函数型相位板的特性进行了深入的研究,并且发现三角函数型相位板不但可以用于扩展景深,而且同时能够作为添加分量来改善其他类型相位板的性能。
第四,以自行设计的低成本、低质量单镜头波前编码成像系统为实验平台,对波前编码成像技术的有效性以及几种不同类型相位板的性能进行了验证。这对于此项技术的应用而言是一个很好的探索,同时也证明即便是在较差的成像系统中,波前编码成像技术也能够起到较好的扩展系统景深的作用。
As is widely known,any imaging system has limited depth of field whose corresponding concept is called depth of focus in image space.Only the objects within the depth of field can be imaged clearly,and other parts being out of the range will be blurred in the image,which leads to the loss of information.The depth of field can be improved to a certain extent by simply decreasing the radius of aperture plane. However,this will sacrifice the system resolution.In 1995,Dr.E.R.Dowski in University of Colorado proposed a novel technique called wave-front coding and solved the dilemma encountered in the conventional imaging system wonderfully.By introducing a suitable phase mask into the aperture plane,the imaging system can be made insensitive to focus errors,defocus related aberrations and the factors causing defocus,such as temperature variation and mechanical instability and so on.It is this modification that greatly extends the depth of field.However,the captured images by wave-front coding system are purposely coded intermediate images and have to be decoded to generate the clear images by using image restoration techniques.Being different from the conventional imaging system,no matter what the object distance is, the defocused point spread function is nearly the same.So,the objects at different distances will be uniformly blurred and this makes the digital post processing easier.
In a word,the wave-front coding system contains two pars:optics and digital filtering.Excellent phase masks and digital restoration methods are the keys to the amazing performance of wave-front coding system.So far,many kinds of phase masks have been suggested,including rotational symmetrical and non-rotational symmetrical.Considering the better performance of non-rotational symmetrical phase masks in enlarging the depth of field,the dissertation majors in several aspects following below,in which the methods adopted and results obtained demonstrate the novelties:
First,by analyzing the characteristics of existing phase masks considering five main aspects,useful instructions are provided when one decides to use the wave-front coding technique,and this is the first time that comprehensive assessments are given. At the same time,it is worth noting that the rarely discussed question of the influence of fabrication precision on system characteristics has been paid special attention and the corresponding results are not only interesting,but also meaningful.
Second,studies on analytical approximate computation of optical transfer function corresponding to the wave-front coding system have been carried out and a method based on fitted polynominal equation is suggested to be used to simplify the complicated mathematical derivations.This method is especially useful to the phase masks whose approximate defocused transfer function can not be obtained by using the computation routine suggested by E.R.Dowski.
Third,by introducing the concept of composite phase masks,new phase masks which can be called sinusoidal-added phase masks have been designed and this enriches the family of phase masks.Lots of simulated and experimental results demonstrate that these new phase masks not only own the ability of enlarging depth of filed,but also are less sensitive to the orginal ones.Besides those,sinusoidal phase mask that is rarely refered in the literatures has been thoroughly investigated and very meaningful results have been obtained as well.
Fourth,based on singlet wave-front coding system,which is low cost and has poor imaging quality,the effectiveness of wave-front coding technique and characteristics of several phase masks have been tested.This is very good for underlying application of wave-front coding technique in real cases and demonstrasts that this technique is still effective in extending the depth of field,even on the condition that imaging quality of the original system was relatively poor.
波前编码成像技术主要由光学设计以及数字图像复原两个方面组成。性能优良的相位掩模板加上强大的复原算法是波前编码成像系统获得惊人效果的关键所在。这项技术发展至今,可以用于景深延拓的相位板层出不穷,且可以分为旋转对称型和非旋转对称型两大类。由于非旋转对称型相位板具有更加优秀的景深扩展能力,所以这类相位板成为了研究的重点和热点,而本文也正是以非旋转对称型相位板为核心来开展相应的研究工作的。
本文的主要工作可以概括为以下四个方面,而其中所使用的方法以及得到的结果就是文章创新性的直接体现。
第一,首次在统一框架下对主流非旋转对称型相位板在景深扩展能力、对初级像差的敏感性、点扩散函数中心偏移效应、中间图像的可恢复性以及加工难度五个方面进行了数值分析,并且以大量翔实的数据为基础建立了波前编码成像系统的性能评价体系原型。尤其值得一提的是,在已有的研究文献中,几乎鲜有加工精度对相位板性能所带来影响的讨论,而本文的工作很好地弥补这个不足。
第二,提出了一种基于多项式面型拟合的方法,可以用来简化波前编码成像系统所对应的离焦传递函数解析表达式的计算,而这对于不适用由E.R.Dowski博士所提出的经典计算方法的相位板而言正好是一种有益的补充。
第三,在充分考察已有相位板特性以及面型特点的基础上,本文提出了几种包括改进的对数型相位板、中心相位补偿型相位板以及叠加正弦分量型相位板在内的新的相位板,并且从理论和实验上证明它们也具有良好的景深扩展能力。此外,本文还首次对文献中鲜有提及的三角函数型相位板的特性进行了深入的研究,并且发现三角函数型相位板不但可以用于扩展景深,而且同时能够作为添加分量来改善其他类型相位板的性能。
第四,以自行设计的低成本、低质量单镜头波前编码成像系统为实验平台,对波前编码成像技术的有效性以及几种不同类型相位板的性能进行了验证。这对于此项技术的应用而言是一个很好的探索,同时也证明即便是在较差的成像系统中,波前编码成像技术也能够起到较好的扩展系统景深的作用。
As is widely known,any imaging system has limited depth of field whose corresponding concept is called depth of focus in image space.Only the objects within the depth of field can be imaged clearly,and other parts being out of the range will be blurred in the image,which leads to the loss of information.The depth of field can be improved to a certain extent by simply decreasing the radius of aperture plane. However,this will sacrifice the system resolution.In 1995,Dr.E.R.Dowski in University of Colorado proposed a novel technique called wave-front coding and solved the dilemma encountered in the conventional imaging system wonderfully.By introducing a suitable phase mask into the aperture plane,the imaging system can be made insensitive to focus errors,defocus related aberrations and the factors causing defocus,such as temperature variation and mechanical instability and so on.It is this modification that greatly extends the depth of field.However,the captured images by wave-front coding system are purposely coded intermediate images and have to be decoded to generate the clear images by using image restoration techniques.Being different from the conventional imaging system,no matter what the object distance is, the defocused point spread function is nearly the same.So,the objects at different distances will be uniformly blurred and this makes the digital post processing easier.
In a word,the wave-front coding system contains two pars:optics and digital filtering.Excellent phase masks and digital restoration methods are the keys to the amazing performance of wave-front coding system.So far,many kinds of phase masks have been suggested,including rotational symmetrical and non-rotational symmetrical.Considering the better performance of non-rotational symmetrical phase masks in enlarging the depth of field,the dissertation majors in several aspects following below,in which the methods adopted and results obtained demonstrate the novelties:
First,by analyzing the characteristics of existing phase masks considering five main aspects,useful instructions are provided when one decides to use the wave-front coding technique,and this is the first time that comprehensive assessments are given. At the same time,it is worth noting that the rarely discussed question of the influence of fabrication precision on system characteristics has been paid special attention and the corresponding results are not only interesting,but also meaningful.
Second,studies on analytical approximate computation of optical transfer function corresponding to the wave-front coding system have been carried out and a method based on fitted polynominal equation is suggested to be used to simplify the complicated mathematical derivations.This method is especially useful to the phase masks whose approximate defocused transfer function can not be obtained by using the computation routine suggested by E.R.Dowski.
Third,by introducing the concept of composite phase masks,new phase masks which can be called sinusoidal-added phase masks have been designed and this enriches the family of phase masks.Lots of simulated and experimental results demonstrate that these new phase masks not only own the ability of enlarging depth of filed,but also are less sensitive to the orginal ones.Besides those,sinusoidal phase mask that is rarely refered in the literatures has been thoroughly investigated and very meaningful results have been obtained as well.
Fourth,based on singlet wave-front coding system,which is low cost and has poor imaging quality,the effectiveness of wave-front coding technique and characteristics of several phase masks have been tested.This is very good for underlying application of wave-front coding technique in real cases and demonstrasts that this technique is still effective in extending the depth of field,even on the condition that imaging quality of the original system was relatively poor.
引文
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