Coordinate system transformations - calibration with examples

master's thesis

• Title (croatian): Transformacije koordinatnog sustava - kalibracija s primjerima
• Author: Ivan Leverić
• Mentor: Zlatko Drmač (mentor)
• Committee member: Zlatko Drmač (predsjednik povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Committee member: Zrinka Franušić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-07-21, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Like many industrial applications, photolithography requires accurate and efficient derivative computation to optimize its resulting product. More specifically, its coordinate system transformation is optimized by error correction in input data, which requires the best possible method to compute the Jacobian matrix of a given transformation. In this work we presented different methods for computing derivatives in the context of coordinate system transformations. We have seen the implementation, as well as the performance differences between the various approaches. It turned out that the simplicity of the numerical methods - finite step and complex step approximations - didn’t come back to bite us, since accuracy wise they proved to be more then acceptable. With that said, AD showed us that an exact and efficient solution can come hand in hand. That was especially true when reverse AD was used as it proved to be the fastest method of all. One knock on the reverse AD is the technical effort required for its implementation, as it forces one to make a decision between a software effort and a slight improvement in efficiency or a simpler, but in general worse, solution.

Abstract (english)

Kao i mnoge industrije, fotolitografija zahtjeva preciznost i učinkovitost u računanju derivacija u svrhu optimizacije finalnog proizvoda. Točnije, korištena transformacija koordinatnih sustava je optimizirana ispravljanjem grešaka u ulaznim podacima, što zahtjeva najbolje moguće metode za računanje Jacobijeve matrice dane transformacije. U ovom radu prezentirali smo razne metode za računanje derivacija u smislu transformacija koordinatnih sustava. Upoznali smo razlike u performansama i implentacijama različitih pristupa. Pokazalo se da jednostavnost numeričkih metoda nije bila kobna, pošto je točnost istih bila više nego zadovoljavajuća. Međutim, automatsko deriviranje nam je pokazalo da egzaktnost i efikasnost mogu ići jedno s drugim. Ta tvrdnja je bila posebice točna za obrnuti AD, koja se pokazala najbržom metodom od svih. Jedina manjkavost te metode je zahtjevnost tehničke implementacije koja je potrebna za izvedbu iste. Zbog toga je potrebno donijeti odluku - uložiti vrijeme i trud za malo poboljšanje u efikasnosti ili prihvatiti malo lošiju metodu, u svrhu jednostavnije izvedbe.

• Keywords: industrial applications; photolithography; Jacobian matrix; reverse AD
• Keywords (croatian): industrija; fotolitografija; Jacobijeva matrica; obrnuti AD
• Language: english
• URN:NBN: urn:nbn:hr:217:641488
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2023-09-14
• Created on: 2022-09-14 09:35:04