CN103063162B - A kind of method of measure portion coherent Gaussian beam Wave-front phase radius - Google Patents
A kind of method of measure portion coherent Gaussian beam Wave-front phase radius Download PDFInfo
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- CN103063162B CN103063162B CN201310010442.XA CN201310010442A CN103063162B CN 103063162 B CN103063162 B CN 103063162B CN 201310010442 A CN201310010442 A CN 201310010442A CN 103063162 B CN103063162 B CN 103063162B
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Abstract
The present invention relates to a kind of method of measure portion coherent Gaussian beam Wave-front phase radius, partially coherent Gaussian beam to be measured has Gauss's associate feature.Light beam to be measured is produced spherical wave front phase place after thin lens focuses on, adopts correlator systematic survey to obtain the initial horizontal of light beam to coherent width
, adopt laser beam analyzer measure respectively obtain light beam initial horizontal to waist width
with the horizontal waist width on exit facet
, process obtains Beam Wave-Front phase place radius to be measured as calculated.The typical partial coherence light beam of measurement provided by the present invention, gather around in fields such as free optical communication, biologic medical, nonlinear medium, inertial confinement fusions and have wide practical use, the measuring method of the partially coherent Gaussian beam Wave-front phase radius provided does not need to use expensive Hartmann Wavefront Sensing sensor, measuring condition is simple, reliable results, with low cost.
Description
Technical field
The present invention relates to a kind of method of measure portion coherent Gaussian beam Wave-front phase radius, that linearly polarized laser bundle frosted glass plate is regulated and controled coherence, with the filtering of G amplitude filter plate, measures optical field distribution and obtain the method for Wave-front phase radius with correlator systematic survey light field coherent width with laser beam analyzer by one.
Background technology
In recent years, partial coherence light beam has wide application prospect due to it in fields such as inertial confinement fusion, optical imagery, optical engineering, material heat treatment, nonlinear optics, light scattering, optical communication, remote remote sensing, laser radar, laser scanning and laser captures, causes very large concern.Gaussian schell model light beam [E. Wolf and E. Collett, " Partially coherent sources which produce same far-field intensity distribution as a laser; " Opt. Commun. 25,293-296 (1978)] as typical partial coherence light beam, its optical field distribution and light field degree of coherence are Gaussian distribution.The general transmission problem with Wigner distribution function process gaussian schell model light beam of tradition; Woods and Cai [Q. Lin and Y. Cai, " Tensor
aBCDlaw for partially coherent twisted anisotropic Gaussian-Schell model beams; " Opt. Lett. 27,216-218 (2002)] proposition Tensor Method processes the paraxonic transmission problem of gaussian schell model light beam.
The double velocity correlation characteristic of partial coherence light beam can characterize with cross-spectral density function.For isotropy, the partial coherence gaussian schell model light beam not having distortion phase place, cross-spectral density can with can, lateral coherence width wide by beam waist and wavefront curvature radius three parameters determine.Partial coherence gaussian schell model light beam is widely applied in fields such as free optical communication, biologic medical, laserresonator, positive and negative refraction rate medium, nonlinear medium, inertial confinement fusion, complicated optical systems.Research finds that partial coherence gaussian schell model light beam degree of coherence can change with the characteristic of transmission medium is different with spectrum, and at free optical communication, there is potential using value the aspects such as medical treatment and information transmission processing.
The with a tight waist wide and coherent width of experiment measuring partial coherence light beam has report, but as the Beam parameters Wave-front phase radius that the another one of partial coherence gaussian schell model light beam is important, its measuring method and device but have no report always, current a kind of many methods are that Hartmann wave front sensor (SHWS) is measured, but this method depends on complexity, expensive measurement equipment, and measurement expense is high.
Summary of the invention
The object of the invention is to the deficiency overcoming prior art existence, provide a kind of measuring condition simple, reliable results, the measuring method of partially coherent Gaussian beam Wave-front phase radius with low cost.
The technical scheme realizing the object of the invention is to provide a kind of method of measure portion coherent Gaussian beam Wave-front phase radius, partially coherent Gaussian beam to be measured has Gauss's associate feature, measuring method comprises the steps: light beam to be measured to produce spherical wave front phase place after thin lens focuses on, and adopts correlator systematic survey to obtain the initial horizontal of light beam to coherent width
, adopt laser beam analyzer measure respectively obtain light beam initial horizontal to waist width
with the horizontal waist width on exit facet
, by formula
obtain the wavefront curvature radius of light beam
r;
Wherein,
kfor wave number, A, B, C and D are astigmatic system transmission matrix;
r 0 for radius-of-curvature before primary wave, by formula
obtain, wherein,
.
The present invention adopts the lateral coherence width of correlator systematic survey light beam, places imaging len, beam splitter and correlator system after light beam tested surface successively, adopts 2
fformation method carries out association detection, the relating value of two-way is carried out Gauss curve fitting, obtains the lateral coherence width of light beam,
ffor the focal length of imaging len.
Measuring method provided by the present invention can utilize the device of following measure portion coherent Gaussian beam Wave-front phase radius, and this device comprises:
Laser instrument produces a branch of random polarization light beam, obtains a branch of linearly polarized laser bundle through the inclined device of line, then focuses on focusing surface after a catoptron and thin lens successively, produces a branch of partial coherence linear polarized beam with Gaussian statistics association;
By described partial coherence linear polarized beam after collimation lens and G amplitude filter plate, obtain the partially coherent Gaussian beam that a branch of collimation has Gauss's association, its wavefront curvature radius is approximately infinitely great;
Again after a condenser lens is assembled, have spherical wave front phase place, spherical wave front phase place radius is measuring object of the present invention; Connect computing machine with laser beam analyzer to measure the partially coherent Gaussian beam light field produced at the difference of light path, measurement result is carried out Gauss curve fitting, obtains the waist width of light beam transversal;
Place imaging len, beam splitter and correlator system after Gaussian beam tested surface successively, correlator system is connected with computing machine, adopts 2
fformation method carries out association detection to light path difference, and namely tested surface to be placed on before imaging len 2
fplace, tested surface will be imaged onto after lens 2
fplace, during measurement, a probe D of fixed correlation detector system
2on optical axis, another D that pops one's head in
1in another curb transversal scanning, the relating value of two-way is carried out Gauss curve fitting, obtain the lateral coherence width of light beam;
The present invention is by the beam waist width on the measurement plane of incidence and incipient beam of light coherent width and transmit a segment distance
zafter beam waist width, in conjunction with the transmission matrix of optical system
,
,
ffor the focal length of condenser lens, after machine processes as calculated, just can obtain the Wave-front phase radius of partially coherent Gaussian beam.
Described laser instrument produces linearly polarized laser bundle through linear polarizer.
Described focusing surface is the one in frosted glass plate, scatterer element or electro-optic crystal element.
A kind of partially coherent Gaussian beam Wave-front phase radius measurement side provided by the invention ratio juris is:
Laser instrument produces a branch of random polarization light beam, a branch of linearly polarized laser bundle is produced through the inclined device of line, focus on frosted glass plate, scatterer element or electro-optic crystal element after a catoptron and a collimation lens again, produce a branch of partial coherence linear polarized beam with Gaussian statistics association; Its association can be expressed as the form of formula (1) below:
In formula,
for light field position vector,
for light beam transversal coherent width.
The partial coherence light beam produced, after a thin lens and G amplitude filter plate, obtains the partially coherent Gaussian beam that a branch of collimation has Gauss's associate feature, and the wavefront curvature radius of this light beam is approximately infinitely great.Now light beam can characterize by formula the following (2):
In formula,
for light beam transversal waist width.
The partially coherent Gaussian beam produced focuses on through another condenser lens 8 again, and the partially coherent Gaussian beam after focusing has spherical wave front phase place, spherical wave front phase place radius
be the object that this patent will be measured, light field cross-spectral density function can be expressed as the form of formula (3) below:
The present embodiment gets the distance of G amplitude filter plate from condenser lens
centimetre, the tested surface after focusing from thin lens distance is
l(need not know).Formula (3) can be expressed as the tensor form of formula (4) below:
In formula,
,
it is plane of incidence light field coordinate vector;
wave number,
for wavelength;
for
the exponent part complex curvature tensor matrix that is concerned with is formula (5):
In formula, I is
rank unit matrix.
After the transmission of astigmatism ABCD optical system, the cross-spectral density function of partial coherence gaussian schell model light beam can be expressed as formula (6) form below:
The value of Det representing matrix determinant in formula;
,
be respectively the arbitrary coordinate vector on exit facet.
for the partial coherence complex curvature tensor on exit facet, there is tensor A BCD formula (7) below:
In formula
with
there is the form of formula (8) below:
with
for astigmatic system transmission matrix.
The form of formula (9) below partial coherence complex curvature tensor matrix on exit facet can also be expressed as:
In formula
,
,
represent the horizontal waist width on exit facet respectively, lateral coherence width and radius-of-curvature.Can be obtained by formula (7):
Convolution (5), (7) and (9), can obtain the relational expression of formula (11), (12) and (13) below respectively:
In formula:
Convolution (11) ~ (14), the wavefront curvature radius that can obtain incipient beam of light is expressed as formula (15):
From above formula, can obtain: choose a primary face and an exit facet; The Wave-front phase radius of initial Gaussian light beam can by measuring the horizontal waist width on exit facet, and the horizontal waist width in primary face and lateral coherence width obtain.Formula (15) is two values, which is right? can be checked by mode below: if measured
,
with
, substitute into formula (15), two wavefront curvature values can be obtained; To obtain again
,
with two
value substitution formula (11), just can obtain the lateral coherence width value on two exit facets, what one of them was identical or close with measured value is just effective value, now corresponding wavefront curvature radius value
be effective value.
Compared with prior art, the invention has the beneficial effects as follows: focus on the spot size on rotating ground glass sheet by thin lens, can regulate and control the coherence of generating portion coherent light beam, the spot size of light beam can be controlled by G amplitude filter plate; This method does not need to use expensive Hartmann Wavefront Sensing sensor, just can obtain the wavefront curvature radius of partial coherence light beam, and measuring condition is simple, reliable results, and cost is low.Partially coherent Gaussian beam particularly as typical partial coherence light beam, is gathered around in fields such as free optical communication, biologic medical, nonlinear medium, inertial confinement fusions and is had wide practical use.
Accompanying drawing explanation
Fig. 1 is the structural representation of a kind of partially coherent Gaussian beam waist width measurement mechanism that the embodiment of the present invention provides;
Fig. 2 is the structural representation of a kind of partially coherent Gaussian beam coherent width measurement mechanism that the embodiment of the present invention provides;
Fig. 3 is a kind of partially coherent Gaussian beam waist width measurement mechanism adopting the embodiment of the present invention to provide, and records incipient beam of light optical field distribution and Gauss curve fitting figure with a tight waist;
Fig. 4 is a kind of partially coherent Gaussian beam coherent width measurement mechanism adopting the embodiment of the present invention to provide, and records incipient beam of light lateral coherence width fitted figure;
Fig. 5 is a kind of partially coherent Gaussian beam waist width measurement mechanism adopting the embodiment of the present invention to provide, and records light beam in transmission
centimetre time optical field distribution figure;
Fig. 6 is a kind of partially coherent Gaussian beam waist width measurement mechanism adopting the embodiment of the present invention to provide, and records light beam in transmission
millimeter,
millimeter,
millimeter,
the optical field distribution figure at millimeter place;
In figure: 1, laser instrument; 2, the inclined device of line; 3, catoptron; 4, thin lens; 5, frosted glass plate; 6, collimation lens; 7, G amplitude filter plate; 8, condenser lens; 9, laser beam analyzer; 10, computing machine; 11, imaging len; 12, beam splitter; 13, correlator system.
Embodiment
Below in conjunction with drawings and Examples, technical solution of the present invention is further described.
Embodiment 1
See accompanying drawing 1, it is the structural representation of a kind of partially coherent Gaussian beam waist width measurement mechanism that the present embodiment provides; Laser instrument 1 produces a branch of random polarization light beam, produces a branch of linearly polarized laser bundle through the inclined device of line 2, then focuses on frosted glass plate 5 after a catoptron 3 and thin lens 4, produces the partial coherence linear polarized beam with Gaussian statistics association; The partial coherence light beam produced, after collimation lens 6 and G amplitude filter plate 7, obtains the partially coherent Gaussian beam of a branch of collimation, and the wavefront curvature radius of this light beam is approximately infinitely great.The partial coherence gaussian schell model light beam produced focuses on through the condenser lens 8 that a focal length is 25 centimetres, and the partially coherent Gaussian beam after gathering has spherical wave front phase place, and the radius of spherical wave front phase place is the parameter that this patent will be measured.Described G amplitude filter plate from condenser lens 8 apart from for
f, the tested surface after focusing from condenser lens 8 is
l.Connect computing machine 10 with laser beam analyzer 9 to measure the partially coherent Gaussian beam light field produced at the difference of light path, measurement result is carried out Gauss curve fitting, the waist width of light beam transversal can be obtained.
See accompanying drawing 2, it is the structural representation of a kind of partially coherent Gaussian beam lateral coherence width of measuring device that the present embodiment provides; Laser instrument 1 produces a branch of random polarization light beam, produces a branch of linearly polarized laser bundle through the inclined device of line 2, then focuses on frosted glass plate 5 after a catoptron 3 and thin lens 4, produces the partial coherence linear polarized beam with Gaussian statistics association; The partial coherence light beam produced, after collimation lens 6 and G amplitude filter plate 7, obtains the partially coherent Gaussian beam that a branch of collimation has Gauss's association, and the Wave-front phase radius of this light beam is approximately infinitely great.The partially coherent Gaussian beam produced focuses on through the condenser lens 8 that a focal length is 25 centimetres, and the partially coherent Gaussian beam after focusing has spherical wave front phase place, and the radius of spherical wave front phase place is the parameter that the present invention needs to measure.Described G amplitude filter plate from condenser lens 8 apart from for
f, the tested surface after gathering from condenser lens 8 is
l(need not know).Finally form 2 with imaging len 11
fimaging optical path, light beam obtains two imaging surfaces after beam splitter 12 equal strength 1:1 beam splitting, places the detecting head D of correlator system 13 respectively on two imaging surfaces
1and D
2, correlator system connects computing machine 10, two optical path signals through interconnected system according calculation, obtains the relating value of two-way light, carries out Gauss curve fitting to relating value, just can obtain the coherent width of imaging surface.
Concrete measuring method is: tested surface is imaged onto lens opposite side 2 by imaging len 11
fdotted line face place, places beam splitter 12 and light beam is divided into the equicohesive two-beam of 1:1 after imaging len, then by two of correlator system detecting head D
1and D
2(dotted line face is 2 from imaging len 11 distance at dotted line face place after placing again beam splitter
f).When measuring coherent width, by detecting head D
1be fixed on the center of light beam, another detecting head D
2along light beam
xdirection moves horizontally, and two paths of signals is done according calculation by correlator, obtains the relating value of two-way light, and relating value is carried out Gauss curve fitting, just can obtain the lateral coherence width of light beam.
See accompanying drawing 3, it adopts a kind of partially coherent Gaussian beam waist width measurement mechanism of providing of the present embodiment, record incipient beam of light optical field distribution (figure a) and Gauss curve fitting figure with a tight waist (figure b); As can be seen from the figure experimental result well meets Gauss curve fitting, obtains incipient beam of light waist width to be
millimeter;
See Fig. 4, it is a kind of partially coherent Gaussian beam coherent width measurement mechanism adopting the present embodiment to provide, and records incipient beam of light lateral coherence width fitted figure; As can be seen from the figure experimental result well meets Gauss curve fitting, obtains incipient beam of light coherent width to be
millimeter.
See Fig. 5, it is a kind of partially coherent Gaussian beam waist width measurement mechanism adopting the present embodiment to provide, and records light beam in transmission
centimetre time optical field distribution figure; As can be seen from the figure experimental result well meets Gauss curve fitting, obtains beam waist width to be
millimeter.
By the initial horizontal that obtains to waist width
millimeter, initial horizontal is to coherent width
millimeter, exit facet
the horizontal waist width of centimeters
the transmission matrix of millimeter and optical system
,
substitute into theoretical formula (15):
Convolution (11):
The wavefront curvature radius of incipient beam of light can be obtained after calculating
centimetre.
By formula (13)
Obtain the wavefront curvature radius of light beam
r.
For the accuracy of checking measurements result, can choose different transmission range and measure waist width, the way repeatedly calculated with regard to mean value carrys out the accuracy of checking measurements value.A kind of partially coherent Gaussian beam waist width measurement mechanism adopting the present embodiment to provide, records light beam respectively in transmission
centimetre,
centimetre,
centimetre,
the optical field distribution figure of centimeters, its result, see accompanying drawing 6, utilizes Gauss curve fitting, obtains corresponding waist width respectively
millimeter,
millimeter,
millimeter and
millimeter.Equally, calculate phase place radius according to formula (15) to be respectively:
centimetre,
centimetre,
centimetre,
centimetre.Calculate phase place radius mean value
centimetre.By error amount expression formula formula (16) error of calculation the following:
Obtain error amount
.As can be seen from error amount, the present invention is feasible according to the measuring method of Theoretical Design, has reliability.
Claims (2)
1. the method for a measure portion coherent Gaussian beam Wave-front phase radius, partially coherent Gaussian beam to be measured has Gauss's associate feature, it is characterized in that measuring method comprises the steps: light beam to be measured to produce spherical wave front phase place after thin lens focuses on, adopt correlator systematic survey to obtain the initial horizontal of light beam to coherent width
, adopt laser beam analyzer measure respectively obtain light beam initial horizontal to waist width
with the horizontal waist width on exit facet
, by formula
obtain the wavefront curvature radius of light beam
r;
Wherein,
kfor wave number, A, B, C and D are astigmatic system transmission matrix;
r 0 for radius-of-curvature before primary wave, by formula
obtain, wherein,
.
2. the method for a kind of measure portion coherent Gaussian beam Wave-front phase radius according to claim 1, it is characterized in that: the lateral coherence width adopting correlator systematic survey light beam, after light beam tested surface, place imaging len, beam splitter and correlator system successively, adopt 2
fformation method carries out association detection, the relating value of two-way is carried out Gauss curve fitting, obtains the lateral coherence width of light beam,
ffor the focal length of imaging len.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6449049B1 (en) * | 2000-03-31 | 2002-09-10 | Nanyang Technological University | Profiling of aspheric surfaces using liquid crystal compensatory interferometry |
| CN1595078A (en) * | 2004-06-30 | 2005-03-16 | 中国科学院上海光学精密机械研究所 | Optical wave front detection device and detection method thereof |
| CN102168955A (en) * | 2011-05-18 | 2011-08-31 | 中国科学院长春光学精密机械与物理研究所 | Method for detecting curvature radius of optical spherical surface |
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| JPH03276044A (en) * | 1990-03-27 | 1991-12-06 | Ricoh Co Ltd | Method and instrument for measuring radius of curvature of curved surface |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6449049B1 (en) * | 2000-03-31 | 2002-09-10 | Nanyang Technological University | Profiling of aspheric surfaces using liquid crystal compensatory interferometry |
| CN1595078A (en) * | 2004-06-30 | 2005-03-16 | 中国科学院上海光学精密机械研究所 | Optical wave front detection device and detection method thereof |
| CN102168955A (en) * | 2011-05-18 | 2011-08-31 | 中国科学院长春光学精密机械与物理研究所 | Method for detecting curvature radius of optical spherical surface |
Non-Patent Citations (2)
| Title |
|---|
| Experimental study of the focusing properties of a Gaussian Schell-model vortex beam;Fei Wang et.;《OPTICS LETTERS》;20110815;第36卷(第16期);3281-3283 * |
| Tensor ABCD law for partially coherent twisted anisotropic Gaussian–Schell model beams;Qiang Lin et.;《OPTICS LETTERS》;20020215;第27卷(第4期);216-218 * |
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