Chapter 1161 He Changed Surveying

Marcel Schmidt would never have thought that many years later, when artificial intelligence research even began to occupy seats in the Nobel Prize and Fields Medal, his remark "neural networks are also mathematics" just for the sake of arguing would become popular and be regarded as a model by researchers in this field.

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

But these are all later stories.

In any case, at this point in time at the end of 2004, "Advances 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 was the winner of the last Fields Medal, and this was his first documented collaborative paper.

Therefore, the focus of the industry quickly shifted from the content of the article itself to the research direction that Chang Haonan was concerned about -

The big guys publishing articles in top journals can lead the trend in themselves.

And chasing hot spots is a feature that most researchers, both Chinese and foreign, have to taste...

Delft University of Technology, the Netherlands.

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

Not far away, his student Qin Shaofeng was concentrating on 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, speaking with a somewhat disappointed tone.

However, before he could finish the rest, Blatt interrupted him in advance:

"It should not match the previous two tests?"

Qin Shaofeng, who was directly guessed the result, was stunned at first, then nodded:

"The same sample to be tested, the same three-dimensional stereo measuring instrument, but the difference between the peak and valley values ​​in the three tests is more than 1μm, and the root mean square is also about 0.3μm, which does not meet the requirements of Party A at all..."

As a higher education institution located in a small lowland country and a city that is not well-known, Delft University of Technology is not only far less famous than giants such as Harvard, MIT, and Oxford, but also far inferior to the University of Amsterdam next door.

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.

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

The project he is currently following up is to develop a new non-contact three-coordinate measurement technology commissioned by Taylor Hobson to detect aspheric 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 contact the surface of the workpiece, it is not suitable for some particularly fragile optical components.

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

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

Faced with the failure that he couldn't remember for the past few months, Qin Shaofeng has realized that it is no longer meaningful to continue to repeat the test.

What is needed now is to change the idea:

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

He first proposed.

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

The first two are not much different for the contact method and the non-contact method, so the accuracy problem of the non-contact method mainly appears in the position offset error -

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

Only by separating the latter through the algorithm can a relatively accurate result be obtained.

So Qin Shaofeng's idea is actually correct.

But the method of recalibrating the observation point...

It is basically equivalent to "restarting and trying" after the computer fails.

It is an attempt with a bit of metaphysics after the specific cause cannot be found.

Although it does work sometimes, it is not good enough for researchers in optical engineering.

So, it was almost immediately rejected by Blatt:

"It is not very meaningful."

He waved his hand and then directly began to analyze the cause of the error to Qin Shaofeng:

"The calibration logic of this equipment is based on the two-dimensional model of the aspheric surface. 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 model curve obtained after two-dimensionalization is not the meridian of the aspheric surface, so simply resetting the observation point will not have any effect..."

Being able to give such a specific explanation before seeing the experimental report made the latter sigh that the old ones are still the best.

But this emotion lasted less than two seconds.

Blatt paused for a moment and 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 there are no rules. The standard equation is generally a quadratic surface superimposed with higher-order term coefficients. In the three-dimensional space, only rotation and translation exist. There is no need to consider rotation along the z-axis, that is, there is only The changes of 6 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 from a classmate in mathematics two days ago that a very well-known scholar just published a paper related to this algorithm, which is to improve the local false optimal problem... and because the content and pure The math was a little bit out of touch, so there was some controversy on their end..."

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 haven't been figured out yet. I may need to have a meeting with them to discuss..."