Chapter 1161 He changed the science of surveying


    Marcel Schmidt would never have imagined that many years later, when artificial intelligence research even began to occupy the Nobel Prize and Fields Medal seats, he would blurt out "Neural networks are also mathematics" just to make excuses. He became popular and was regarded as Guigao by researchers in the field.


    Even Schmidt himself became one of the objects of worship in some rituals to appease the server machine soul.


    But these are all things for later.


    In any case, at this point in time in late 2004, "Progress in Mathematics" chose to publish a paper related to global optimization and data models, which was big news that could cause a slight earthquake in the industry.


    Fortunately, one of the authors of the paper is the winner of the last Fields Medal, and this is his first well-documented collaborative paper.


    Therefore, the focus of the industry quickly transitioned from the content of the article itself to the research direction that Chang Haonan is concerned about—


    When a big boss publishes an article in a top journal, he or she can set the trend.


    Chasing hot topics, whether at home or abroad, is a feature that most researchers have to taste...


    Delft University of Technology, Netherlands.


    Professor Joseph Blatt was standing in front of a white light interferometer, looking through a series of test results displayed on the computer screen with a complicated expression.


    Not far away, his student Qin Shaofeng was immersed in checking a test report that had just been spit out by the device in front of him.


    "Professor, the results have been compared..."


    A few minutes later, Qin Shaofeng took off his glasses and put them aside, and spoke with a somewhat disappointed tone.


    However, before he could say what was to follow, Brat interrupted him in advance:


    "It shouldn''t match the first two tests?"


    Qin Shaofeng, who was directly guessed the result, was stunned for a moment, then nodded:


    "The same sample being tested, the same three-dimensional measuring instrument, but the difference between the peak and valley values ??in the three tests was more than 1 μm, and the root mean square was about 0.3 μm, which completely failed to meet Party A''s requirements..."


    As an institution of higher learning located in a small low-lying country and in a city that is not well-known, Delft University of Technology is not only far less famous than behemoths such as Harvard, Massachusetts, and Oxford, but is far less famous than the University of Amsterdam next door. Far worse.


    However, it has considerable strength in optics and optical engineering.


    And Joseph Blatt is one of the most outstanding scholars in this field.


    He worked for Philips and ASML in the 1970s and 1980s, and moved to academia in 1988. He then continued to make a series of outstanding contributions in the fields of optical imaging and optical storage technology.


    and is one of the founders and current president of the European Optical Society.


    The project he is currently following up on is to develop a new non-contact three-coordinate measuring technology commissioned by Taylor Hobson to inspect the production of aspherical lenses with a peak-to-valley (PV) value better than 0.1μm. .


    This accuracy is not exaggerated for contact measurement technology based on atomic force analysis, but because the probe needs to be in contact with the surface of the workpiece, it is not suitable for some particularly fragile optical components.


    In contrast, non-contact measurement using interference methods and geometric ray methods is obviously much friendlier.


    Of course, it is much more difficult to achieve the same accuracy as contact measurement.


    Facing this failure that he couldn''t remember for the past few months, Qin Shaofeng had realized that there was no point in continuing repeated experiments.


    What we need now is to change our thinking:


    "Should we consider recalibrating the public observation points of the equipment, so that the position offset error may be reduced?"


    He suggested first.


    The errors in the surface detection process mainly come from three aspects: motion axis error, probe error and position offset error.


    There is not much difference between the first two methods between the contact method and the non-contact method. Therefore, the accuracy problem of the non-contact method mainly occurs in the position offset error -


    Since there is no probe that can directly contact the surface and directly determine the reference origin of measurement, the error data captured by the non-contact device is essentially equivalent to the superposition of surface error and position offset error.


    Only by separating the latter through algorithms can relatively accurate results be obtained.


    So Qin Shaofeng''s idea is actually correct.


    But the method of recalibrating the observation point...


    It''s basically equivalent to "try restarting" after a computer failure.


    It was an attempt with a bit of metaphysics after I really couldn''t find the specific reason.


    Although sometimes it does work wonders, for researchers majoring in optical engineering, it is a bit unsightly.


    Therefore, Blatter rejected it almost immediately:


    "It doesn''t mean much."


    He waved his hand, and then directly began to analyze the reasons for the error for Qin Shaofeng:


    "The current calibration logic of this equipment is based on the two-dimensional aspheric model. Although some corrections have been made using the Gauss-Newton method, in essence, the measured center of the aspheric surface is still not the center of the actual surface, and the two-dimensional The model curve obtained after transformation is not an aspheric meridian, so just resetting the observation points will not be effective..."


    Being able to give such a specific explanation before seeing the experimental report made the latter couldn''t help but sigh, after all, **** is still hotter. But this emotion lasted less than two seconds.


    I heard Brat pause for a moment, and then continued:


    "And more importantly, I tried it last night and it didn''t work..."


    “…”


    The filter instantly shattered.


    Of course, work still has to go on.


    After some thinking, Qin Shaofeng thought of a new way:


    "Then if we upgrade this equipment to a control computer with better performance, can we skip the two-dimensional model calculation step and directly use the three-dimensional correction algorithm to obtain the coordinates of the circle center and aspheric surface in the space?"


    This time, it was not directly rejected.


    "The problem with the three-dimensional correction algorithm is that it is prone to local convergence... resulting in outliers with particularly outrageous errors, which is very difficult to accept in industrial production..."


    Blatter has obviously been thinking about this for a long time:


    "Actually, if we can overcome the local convergence problem, we only need to generate three-dimensional aspheric data with position errors and surface shape errors through simulation, and then compare the generated coordinate points with the standard aspheric equations to obtain each The error of the coordinate point, and finally using the principle of minimum root mean square error, the corresponding position error can be iteratively optimized..."


    In fact, aspheric surfaces do not mean that they are irregular. Its standard equation is generally a quadratic surface superimposed with higher-order term coefficients. In three-dimensional space, only rotation and translation exist, and there is no need to consider rotation along the z-axis, that is, there are only 6 The change of degrees of freedom, as for the position parameters, can be expressed by two third-order matrices containing second-order partial derivatives and three error terms.


    Therefore, the final problem can be summarized as: using a reasonable global optimization algorithm to optimize the objective function to minimize the error function value.


    And Qin Shaofeng''s foundation is indeed solid. After listening to his mentor''s ideas, he quickly captured some new ideas.


    However, it is still vague:


    "So it was said before that the two-dimensional model still fails to achieve results after optimization, because the Gauss-Newton method is not positive definite in the process of solving the optimal solution?"


    "Not quite."


    Bratt shrugged helplessly:


    "In fact, someone in Japan has already used the Levenberg-Marquardt method, which is positive definite in solving the Hessian matrix, for three-dimensional measurement, but the effect still does not meet the expected value."


    “Levenberg-Marquardt method…”


    This term finally allowed Qin Shaofeng to completely grasp the flash of inspiration, and his whole body became energetic instantly:


    "I heard it from a classmate majoring in mathematics two days ago. It seems that a very well-known scholar has just published a paper related to this algorithm, which is to improve the local false optimal problem... and because the content is similar to pure mathematics It was a bit out of touch, so it caused some controversy on their side..."


    Bratt himself actually has some mathematical skills, but he is indeed not comparable to serious mathematicians.


    But it was enough for him to realize the value of this paper in the field of optics.


    "If you have more detailed information, I would like to take a look at this paper."


    he asked almost glaringly.


    "I have a link to the paper''s web page..."


    Qin Shaofeng said, taking off his gloves and turning around to go to the office to get his computer.


    However, Brat couldn''t wait any longer and immediately pointed to his computer next to him:


    "Maybe you can just use this..."


    A few minutes later, a paper with a thickness of about twenty pages was handed into Blatt''s hands.


    "For a mathematics paper, it is indeed a bit too long."


    He took it half-jokingly.


    Qin Shaofeng''s answer was quite serious:


    "My classmate said that if you are only interested in the Levenberg-Marquardt method itself, you only need to read the first half..."


    "knew…"


    Brat didn''t even raise his head, but just waved his hand towards Qin Shaofeng, indicating that the latter could go to rest first.


    However, Qin Shaofeng, who breathed a sigh of relief, had just returned to his seat in the office when the phone next to him suddenly rang.


    "Qin, go and contact Taylor Hobson Company for me."


    "I just said that I have a new technical solution...but some specific details have not been figured out yet. I may need to have a meeting with them to discuss it..."


    (End of chapter)