When first order paraxial optics is expanded to third order optics (i.e. sin x~ x-x3/3! instead of sin x~x) , these 5 optical aberrations result in. What is the rigorous mathematical proof that, simultaneous correction of the five aberrations would cause violation of laws of reflection and/or refraction? and what are the mathematical prerequisites to understand the topic(say, beyond undergraduate freshman physics and mathematics knowledge)?
There are a huge number of examples of optical systems that correct all of these aberrations tremendously well as well as other aberrations of much higher order than third order. The lens on any halfway decent camera is very well corrected with low distortion. It may be that theoretical perfection is impossible, but we have a scale, the diffraction limit, against which to measure what is close enough to perfection. It is normal for a a good lens design to show nearly diffraction limited performance for the entire visible spectrum across the entire field of view.
When it is said that it is impossible to correct this or that, usually various constraints are also mentioned. It is impossible to correct all of the Seidel aberrations WITH A SINGLE SPHERICAL LENS or it is impossible to correct chromatic aberration WITH A SINGLE OPTICAL MATERIAL or some other constraint like that.
There are a huge number of examples of optical systems that correct all of these aberrations tremendously well as well as other aberrations of much higher order than third order. The lens on any halfway decent camera is very well corrected with low distortion. It may be that theoretical perfection is impossible, but we have a scale, the diffraction limit, against which to measure what is close enough to perfection. It is normal for a a good lens design to show nearly diffraction limited performance for the entire visible spectrum across the entire field of view.
When it is said that it is impossible to correct this or that, usually various constraints are also mentioned. It is impossible to correct all of the Seidel aberrations WITH A SINGLE SPHERICAL LENS or it is impossible to correct chromatic aberration WITH A SINGLE OPTICAL MATERIAL or some other constraint like that.
Dear Mr. Sumit,
You can correct all 5 classical optical aberration simultaneously.
Generally speaking, the all optical aberration can be expressed as the combination of different orders of Zernike functions, and in wave optics, they are nothing more than some special phase distribution added on the beam's wavefront.
As long as the phase of the aberration can be measure, you can correct them through wavefront shaping, and mathematically, this process is to add a compensation phase term to the beam's wavefront to cancel out the impact of aberrations.
For example, in adaptive optics, one uses a wavefront sensor to measure the phase of aberrations, and then uses a deformable mirror to correct them.
There are also many different methods to correct the optical aberration in field of computational imaging.
Best regards.
I totally agree with both my colleagues. Simply speaking:
From a theoretical view point:
You have a certain amount of power in the optical beam in the different abberations. Describing the wavefront in terms of Seidel, Zernike or whatever polynomials, only means to distribute the power into the (hopefully orthogonal) polynomials. From a theoretical view point there is no rule not to redistribute the power (with a small exception). Thus you can correct the chosen orders by transferring the power into higher polynomials.
From a practical view point:
For a perfectly known, stable (not transient) wavefront a free-form shape optics can be designed that does the job. However, the wavefront is never known fully and is never really stable and the wavefront-correction mechanism has to compensate this. The wavefront-correction does include always real systems... and so on.
To describe with an other "theory": You have a control theory related problem, as you need to feedback the information of the wavefront into your wavefront-correction mechanism, which can only behave in theory perfect.
Regarding the other part of the questions:
Beyond the aberration-theory and if practical, wavefront-sensors, spatial light modulators and so on, I recommend to put in the perspective of control theory...
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