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SLO: Laboratoř interferometrie


Jedním z pracovníků skupiny klasické optiky je Pavel Pavlíček. Zabývá se výzkumem v oblastech: interferometrie v bílém světle, profilometrie s prostorovou koherencí a interferometrie se dvěma vlnovými délkami.

Interferometrie v bílém světle

ilustrační fotografieInterferometrie v bílém světle je ověřená metoda pro měření 3D topografie technických drsných povrchů a hladkých (odrazných) povrchů s vysokou (u drsných povrchů s mikrometrovou a u hladkých s nanometrovou) přesností. V této metodě se obvykle používá Michelsonův interferometr, jehož zdroj světla má široké spektrum (bílé světlo). Princip měření spočívá v hloubkovém skenování během nějž je měřený předmět posouván v podélném směru. Tímto způsobem se mění rozdíl optických drah mezi předmětovým a referenčním svazkem v přesně definovaném rozsahu. Na výstupu interferometru je umístěna maticová kamera jako mnohonásobný detektor. Intenzita světla zaznamenaná pro různé polohy měřeného předmětu tvoří interferogram. Z poloh interferogramů zaznamenaných všemi pixely kamery je možné sestavit 3D topografickou mapu měřeného předmětu.

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Profilometrie s prostorovou koherencí

ilustrační fotografieProfilometrie s prostorovou koherencí je metoda pro měření geometrického tvaru předmětu. Nejdůležitější částí měřicí sestavy je Michelsonův interferometr osvětlený monochromatickým plošným zdrojem světla. Vlivem prostorové koherence se na výstupu interferometru objeví korelogram, který je možné použít pro měření geometrického tvaru předmětu. Tento korelogram tvoří analogii korelogram známého z interferometrie v bílém světle, který je způsoben časovou koherencí.

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Interferometrie se dvěma vlnovými délkami

ilustrační fotografiePJednou z nevýhod interferometrie v bílém světle je, že zdroje se širokým spektrem mají nízký jas. Obejít tuto nevýhodu je možné tím, že se zdroj se širokým spektrem nahradí dvěma lasery s různými vlnovými délkami. Při měření tvaru je měřený předmět posouván podél optické osy a přitom je na výstupu interferometru zaznamenáván interferogram, který má typický tvar záznějového obrazce. Vyhodnocením takového interferogramu je možné určit podélnou souřadnici povrchu předmětu a tak změřit jeho geometrický tvar. Díky vysokému jasu laserů je možné měřit i tvar předmětů se slabě odrážejícím povrchem. Vhodným výběrem dvou nebo více laserů je možné tvarovat koherenční funkci podle požadavků měřicí úlohy.

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Interferometrie v bílém světle

 

papers

 

P. Pavlíček, O. Hýbl: White-light
interferometry on rough surfaces - measurement uncertainty caused by surface
roughnes,

Applied Optics 47, 2941-2949 (2008).

 

Abstract:

White-light
interferometry measuring an optically rough surface commonly does not resolve
the lateral structure of the surface. This means that there are height
differences within one resolution cell that exceed one-fourth of the wavelength
of the light used. Thus the following questions arise: Which height is measured
by white-light interferometry? How does the surface roughness affect the
measurement uncertainty? The goal of the presented paper is to answer these
questions by means of numerical simulations. Before the aforementioned
questions can be answered, the distribution of the intensity of individual
speckles, the influence of surface roughness, and the spectral width of the
light source used are discussed.

 

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P. Pavlíček, G. Häusler: White-light
interferometer with dispersion: an accurate fiber-optic sensor for the
measurement of distance,

Applied Optics 44, 2978-2983 (2005).

 

Abstract:

We present a fiber-optical
sensor for distance measurement of smooth and rough surfaces that is based on
white-light interferometry; the sensor measures the distance from the sample
surface to the sensor head. Because white light is used, the measurement is
absolute. The measurement uncertainty depends not on the aperture of the
optical system but only on the properties of the rough surface and is commonly
~1 μm. The measurement range is approximately 1 mm. The sensor includes no
mechanical moving parts; mechanical movement is replaced by the spectral
decomposition of light at the interferometer output. The absence of mechanical
moving parts enables a high measuring rate to be reached.

 

_______________________

 

P. Pavlíček: Height profile measurement by
means of white light interferometry,

Proceedings of the society of photo-optical
intstrumentation engineers (SPIE), volume: 5259, pages: 139-144 (2003) 13th
Polish-Czech-Slovak Conference on Wave and Quantum Aspects of Contemporary
Optics, September 9-13, 2002 Krzyzowa, Poland.

 

Abstract:

White light
interferometry is an established method for height profile measurement of
objects. This method, unlike classical interferometry, can be used for
measurement of objects with rough surface, which is an important advantage.

The white light interferometer is in
principle a Michelson interferometer with a broad-band light source and a CCD
camera as a detector. The Michelson interferometer has the object to be
measured in one arm and the reference mirror in the other arm. Due to the reflection
on the rough surface, a speckle pattern arises in the detector plane. This
pattern is superimposed on the reference wave. The phase in particular speckle
is random, but it remains approximately constant within one speckle. This
renders the white light interference observable, if the optical path lengths of
the two arms differ less than the coherence length.

The object to be measured is mounted on a
micropositioner for translating in the longitudinal direction. Gradually, as
parts of the object surface cross the reference plane, the white light
interference is observable in the corresponding speckles. The position of the
micropositioner, in which the interference is maximal, is stored for each pixel.
This value for each pixel of the object image describes the geometrical shape
of the measured object.

The measuerement range is theoretically unlimited,
practically it is limited by the range of the micropositioner. The longitudinal
uncertainty does not depend on the parameters of the optical setup, its value
is given by the roughness of the measured surface. The height profile of the
object is measured during one measurement process, unlike the scanning
profilers. The illumination and the observation are coaxial, which avoids shadows.

 

_______________________

 

P. Pavlíček, J. Soubusta:
Measurement of the influence of dispersion on white-light interferometry,

Applied Optics 43, 766-770 (2004).

 

Abstract:

White-light
interferometry is a well-established method for measuring the height profiles
of samples with rough as well as with smooth surfaces. Because white-light
interferometry uses broadband light sources, the problem of dispersion arises.
Because the optical paths in the two interferometer arms cannot be balanced for
all wavelengths, the white-light correlogram is distorted, which interferes
with its evaluation. We investigate the influence of setup parameters on the
shape of the correlogram. Calculated values are compared with experimental
results.

 

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P. Pavlíček, J. Soubusta:
Theoretical measurement uncertainty of white-light interferometry on rough
surfaces,

Applied Optics 42, 1809-1813 (2003).

 

Abstract:

A great advantage of the
white-light interferometry is that it can be used for profile measurement of objects
with a rough surface. A speckle pattern that arises in the image plane allows
one to observe the interference; however, this pattern is also the source of
the measurement uncertainty. We derive the theoretical limits of the
longitudinal uncertainty by virtue of the first-order statistics of the speckle
pattern. It is shown that this uncertainty depends on the surface roughness of
the measured object only; it does not depend on the setup parameters.

 

diploma theses:

 

Ondřej Hýbl: Měření
tvaru předmětu pomocí interferometrie v bílém světle se spektrálním
rozkladem (2005).

 

Profilometrie s prostorovou koherencí

 

papers:

 

P. Pavlíček, M. Takeda: Similarities and
Differences between Spatial Coherence Profilometry and White-light
Interferometry,

International Conference on Advanced Phase
Measurement Methods in Optics and Imaging, book series AIP Conference
Proceedings, volume: 1236, pages: 161-166 (2010).

 

Abstract:

Spatial coherence
profilometry is a method that uses a Michelson interferometer illuminated by a
quasimonochromatic spatially extended light source to measure the shape of
objects. Because of the spatially extended light source, this method takes
advantage of spatial coherence of the light. Thus spatial coherence
profilometry appears to be a spatial coherence analogy to white-light
interferometry which is a reliable and proved method for the measurement of the
shape of objects. White-light interferometry usually uses a Michelson
interferometer illuminated by a polychromatic point-like light source and so is
based on temporal coherence. Though these both measurement methods look similar
they show some significant differences. By means of theoretical analysis and
experiments we investigate what is similar and where are the differences
between these both methods.

_______________________

 

P. Pavlíček, M. Halouzka, Z. Duan, M.
Takeda: Spatial coherence profilometry on tilted surfaces,

Applied optics 48, H40-H47 (2009).

 

Abstract:

The influence of tilted
surfaces on the measurement of shape by spatial coherence profilometry is
investigated. Based on theoretical analysis and experimental results, the
systematic measurement error caused by surface tilt is determined. The
systematic measurement error depends not only on the tilt angle but also on the
parameters of the experimental setup. The theoretical analysis and the
experiments show the similarities and differences between spatial coherence
profilometry and white-light interferometry. We also suggest the conditions to
obtain correct measurements by use of spatial coherence profilometry.

 

_______________________

 

P. Pavlíček, Z. Duan, M. Takeda: Spatial
coherence profilometry,

Proceedings of the society of photo-optical
intstrumentation engineers (SPIE), volume: 6609, pages: 60916-60916 (2007) 15th
Czech-Polish-Slovak Conference on Wave and Quantum Aspects of Contemporary
Optics, September 11-15, 2006 Liberec, Czech Republic.

 

Abstract:

Spatial
coherence profilometry is a method for measurement of the geometrical form of
objects. In addition to the two lateral coordinates x and y, it measures the
longitudinal coordinate z. In this way the complete 3D description of the
object's surface is acquired.

The main piece
of the presented method is a Michelson interferometer illuminated by a
monochromatic spatially extended light source. The surface of the object whose
geometrical form should be measured is used as one mirror of the Michelson
interferometer. By moving of the measured object along the optical axis, the
intereference is observable only if the object's surface occurs in the vicinity
of the so-called reference plane. The reference plane is given by the position
of the object mirror when the Michelson interferometer is balanced. The
described effect follows from the form of the spatial coherence function
originated by the spatially extended light source.

If the intensity
at the output of the interferometer is recorded as a function of the position
of the measured object, a typical correlogram arises. This correlogram is
similar to that known with white-light interferometry. From the maximum of the
correlogram, the z coordinate of the object's surface can be determined.
Usually a CCD camera is used as the detector at the output of the Michelson
interferometer. Then z coordinates of many surface points are parallel
measured in the course of one measurement procedure and the 3D description of
the object's surface is acquired. The scanning in the lateral direction is not
necessary. Thus the described method provides a spatial coherence analogy to
white-light interferometry which is based on temporal coherence. Unlike to the
white-light interferometry, the described method does not require a broadband
light source, the interferometer is illuminated by a monochromatic light
source, usually a laser.

 

diploma theses:

 

Marek Halouzka: Optical 3D sensors for
shape measurement of objects (2008).

 

Marek Šimíček: Určování topologie povrchů
pomocí analýzy zaostření (2007).

 

Interferometrie se dvěma vlnovými délkami

 

papers:

 

P. Pavlíček, G. Häusler: Measurement
of the shape of objects by the interferometry with two wavelengths, Proceedings
of The 6th International Workshop on Advanced Optical Metrology, Springer,
pages 339 - 344, September 13 - 16, 2009, Nürtingen, Germany.

 

White-light
interferometry is an established method for the measurement of geometrical
shape of object with smooth or rough surface. One of the disadvantages of
white-light interferometry is that the required broadband light sources suffer
from a low luminance. This shows up when the shape of object with a weakly
reflecting surface is measured or when the measured area is large. One way to
overcome this disadvantage is to replace the broadband light source by two (or
more) lasers with various wavelengths.

If
the broadband light source is replaced by two lasers with various wavelengths,
a typical beat pattern arises at the output of the interferometer instead of
white-light interferogram. The beat pattern can be used for the determination
of the position of the object's surface in a similar way as white-light
interferogram. Unlike to white-light interferogram, the beat pattern is
periodic and therefore the unambiguity range is limited.

 

diploma theses:

 

Vladimír Kocour: Měření tvaru předmětů pomocí
interferometrie se dvěma vlnovými délkami (2010).

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