Beam Expander Basics: Not All Spots Are Created Equal

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1 EARNING UNERSTANING INTROUCING APPYING Beam Expander Basics: Nt All Spts Are Created Equal A P P I C A T I O N N O T E S

2 BEAM EXPANERS A laser beam expander is designed t increase the diameter f a cllimated input beam t a larger cllimated utput beam. Beam expanders are used in applicatins such as laser scanning, interfermetry, and remte sensing. Cntemprary laser beam expander designs are afcal systems that develped frm well-established ptical telescpe fundamentals. In such systems, the bject rays, lcated at infinity, enter parallel t the ptical axis f the internal ptics and exit parallel t them as well. This means that there is n fcal length t the entire system. THEORY: TEESCOPES Optical telescpes, which have classically been used t view distant bjects such as celestial bdies in uter space, are divided int tw types: refracting and reflecting. Refracting telescpes utilize lenses t refract r bend light while reflecting telescpes utilize mirrrs t reflect light. Refracting telescpes fall int tw categries: Keplerian and Galilean. A Keplerian telescpe cnsists f psitive fcal length lenses that are separated by the sum f their fcal lengths (Figure 1. The lens clsest t the surce image, r the bject being viewed, is called the bjective lens while the lens clsest t the eye, r image created, is called the image lens. A Galilean telescpe cnsists f a psitive lens and a negative lens that are als separated by the sum f their fcal length (Figure 2. Hwever, since ne f the lenses is negative, the separatin distance between the tw lenses is much shrter than in the Keplerian design. Please nte that using the Effective Fcal ength f the tw lenses will give a gd apprximatin f the ttal length, while using the Back Fcal ength will give the mst accurate answer. Figure 1: Keplerian Telescpe Figure 2: Galilean Telescpe

3 THEORY: TEESCOPES (CONT. The Magnifying Pwer r the inverse f the magnificatin f the telescpe is based upn the fcal lengths f the bjective and eye lenses. (1 Magnifying Pwer (MP = 1 magnificatin (M If the magnifying pwer is greater than 1, the telescpe magnifies; if the magnifying pwer is less than 1, the telescpe minifies. (2 MP = - Fcal ength Fcal ength THEORY: ASER BEAM EXPANERS In a laser beam expander design, the placement f the bjective and image lenses is reversed. In the Keplerian beam expander design, the cllimated input beam fcuses t a spt between the bjective and image lenses, prducing a pint within the system where the laser s energy is cncentrated (Figure 3. The fcused spt heats the air between the lenses, deflecting light rays frm their ptical path, which can ptentially lead t wavefrnt errrs. Fr this reasn, mst beam expanders utilize the Galilean beam expander design r a variant f it (Figure 4. i qi q When using the Keplerian r Galilean design in laser beam expander applicatins, it is imprtant t be able t calculate the utput beam divergence, which determines the deviatin frm a perfectly cllimated surce. The beam divergence is dependent upn the diameters f the input and utput laser beams. i Figure 3: Keplerian Beam Expander Figure 4: Galilean Beam Expander (3 Input Beam ivergence ( Output Beam ivervenge (θ O = Output Beam iameter ( Input Beam iameter ( I The Magnifying Pwer (MP can nw be expressed in terms f the Beam ivergences r Beam iameters. (4 (5 MP = MP = θ O I

4 THEORY: ASER BEAM EXPANERS Interpreting the abve equatins, ne sees that while the Output Beam iameter ( increases, the Output Beam ivergence (θ O decreases and vice versa. Therefre, if yu use the beam expander as a beam minimizer, the beam diameter will decrease but the divergence f the laser will increase. The price t pay fr a small beam is a large divergence angle. In additin t the abve, it is imprtant t be able t calculate the utput beam diameter at a specific wrking distance (. The utput beam diameter is a functin f the input beam diameter and the beam divergence after a specific wrking distance (, (Figure 5. I 2 Figure 5 (6 = I + ( tan aser beam divergence is specified in terms f a full angle, therefre, the abve equatin is expressed in terms f and nt /2. Since a beam expander will increase the input beam by the Magnifying Pwer and decrease the input divergence by it as well, substituting equatins (4 and (5 int (6 results in the fllwing. (7 (8 = (MP x I + tan MP = (MP x I + ( tan θ O APPICATION EXAMPES EXAMPE 1 Numerical example t explre previusly mentined beam expander equatins. Initial Parameters: Beam Expander Magnifying Pwer = MP = 10X Input Beam iameter = 1mm Input Beam ivergence = 1mrad Wrking istance = = 100m /vides

5 Calculated Parameters: (9 Cmpare this t the Beam iameter withut using a beam expander by using equatin (6. (10 = (MP x I + tan = I + ( tan Althugh a beam expander will increase the input laser beam by a specific expansin pwer, it will als decrease MP = (10 x 1mm + 100,000mm x tan EXAMPE 1 (CONT. 1mrad 10X = 20mm = 1mm + (100,000mm x tan(1mrad= 101mm EXAMPE 2 the divergence by the same expansin pwer, resulting in a smaller cllimated beam at a large distance. Theretical example fr reducing a laser beam s divergence at a lng wrking distance using a beam expander. In additin t imprving beam cllimatin, beam expanders can be used t fcus laser beams. The fllwing table shws istance 1.2m 1.5m 2.5m 5.0m 10m Beam Expander Pwer 5X 10X 20X μm μm μm μm μm μm μm μm μm μm μm μm μm μm μm simulated fcusing perfrmance fr the 5X, 10X and 20X beam expanders. The spt sizes are given in units f micrns and are calculated using a 0.63mm diameter laser beam at 632.8nm assuming M 2 =1 and a perfectly cllimated input beam. Nte: The 1/e 2 spt diameters listed were calculated frm the equatin: 2 * f/# * wavelength, where f/# is the wrking f/# EMUNPTICS PROUCTS Examples f the applicatin f the Galilean telescpe design t laser beam expanders can be fund in several Edmund Optics prducts, all f which can be used t cllimate and fcus laser beams. Our Fixed Pwer HeNe Beam Expanders is a simple Munting Thread (2 x M6 x 1.0 Munting Hles 2 x ¼-20 Munting Hles 50.0mm tw-lens design, cnsisting f a negative lens and achrmatic lens. rawing f the internal ptical elements is shwn fr reference. Edmund Optics als ffers a CO 2 Adjustable Beam Expander that utilizes tw Zinc Selenide lenses t expand a 10.6μm laser beam. Cnstructin is similar t ur Fixed Pwer HeNe Beam Expanders and aser ide Beam Expanders. Our TECHSPEC Fixed Pwer aser Beam Expander imprves upn the simple tw-lens design with a prprietary multielement lens design that enhances its ability t create a cllimated r fcused laser beam diameter at a lng wrking distance. Nte: Select laser ptic prducts are nt available in all lcatins. Please cntact yur Reginal Sales Office t inquire abut availability.

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