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Design and construction of a cost-efficient Arduino-based mirrorgalvanometer system for scanning optical microscopy

Jen-Feng Hsu,a) Shonali Dhingra, and Brian D’Ursob)

Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

(Received 19 November 2014; accepted 15 November 2016)

Mirror galvanometer systems (galvos) are commonly employed in research and commercial

applications in areas involving laser imaging, laser machining, laser-light shows, and others. Here,

we present a robust, moderate-speed, and cost-efficient home-built galvo system. The mechanical

part of this design consists of one mirror, which is tilted around two axes with multiple surface

transducers. We demonstrate the ability of this galvo by scanning the mirror using a computer, via

a custom driver circuit. The performance of the galvo, including scan range, noise, linearity, and

scan speed, is characterized. As an application, we show that this galvo system can be used in a

confocal scanning microscopy system. VC 2017 American Association of Physics Teachers.

[http://dx.doi.org/10.1119/1.4972046]

I. INTRODUCTION

A galvanometer is a sensitive electromechanical actuatorthat is used to detect feeble electrical currents on the order ofmicroamps.1,2 It works on the principle of a current-carryingcoil experiencing a torque when placed in an external mag-netic field, due to its effective magnetic dipole moment l. Amechanical pointer, which is a part of the coil, moves over ascale in response to the presence of an electrical current,proving a visible response.

In place of a pointer, a “galvo” uses a laser beam reflectedoff a movable mirror. Galvo systems are widely used inoptical setups that require precision control, such as in posi-tioning and scanning of laser beams. Galvo systems findextensive use in various scientific and non-scientific equip-ment used for processes such as laser imaging, laser machin-ing, laser welding, laser ablation, laser cleaning, waferdicing, laser-light shows, etc.3–9

One common use for a galvo system is in confocal laserscanning microscopy (CLSM). This technique is used toobtain high-resolution optical images of topologically com-plex objects by rastering a laser beam over individual two-dimensional surfaces of the object at different depths, andcollecting only the in-focus scattered or photoluminescentlight.10,11 The most common commercial implementation ofthe two-dimensional rastering is the two-closely-spaced-scan-mirrors arrangement,12 in which two mirrors are tiltedin orthogonal directions.

A typical commercial galvo system (for example, ThorlabsGVS012) has features such as low drift and precise positioncontrol. These features are achieved by a servo motor controlsystem instead of a single magnet and a coil as originallydeveloped. The servo systems are closed-loop systems, so themotor positions are internally measured and fed back to calcu-late the errors, which are in turn corrected by further adjustingthe motor. It has a full swing angle of up to 620� (dependingon the beam diameter) and a smaller swing of 60:2� for a fast(�1 kHz) scan.13 The cost for such a commercial unit could be�$2500 or more. Thus, building a microscope system aroundsuch a unit could lead to substantially high costs, often notfeasible for use in educational laboratories. Furthermore, thecomplex position sensor system used by the servo controllerrequires precise internal alignment, making repair and mainte-nance expensive. Due to these reasons, a simple, robust, andinexpensive galvo system could be very useful.

Here, we present such an affordable alternative to a com-mercial galvo unit, which has a robust and accessible design,making it easy to repair and maintain. It is an open-loopsystem, as opposed to a closed-loop system as in a typicalcommercial unit, meaning there is no internal measurementand feedback of the galvo mirror position. Thus, this galvomay be subject to more drift and position error. Because ofits simplicity, building such a galvanometer system can be agreat educational exercise in intermediate and advancedundergraduate level courses, requiring only basic mechanics,electronics, and programming skills and techniques.

68 Am. J. Phys. 85 (1), January 2017 http://aapt.org/ajp VC 2017 American Association of Physics Teachers 68

We describe the concept and setup of the galvo system inSec. II. Characterizations of some of its properties, such asthe mirror size, scan range, noise, linearity, center of rota-tion, and frequency response, are reported in Sec. III.Finally, we present an application of this galvo system—con-focal scanning microscopy—which is performed in conjunc-tion with other optical elements such as lasers, lenses,optical fibers, and microscope objective, in Sec. IV.

II. DESIGN AND CONSTRUCTION OF THE GALVO

A. Basic concept

For simplicity, the galvo system presented here uses onemirror, as opposed to two used in many commercial models.Surface transducers, which are originally designed for audiotransduction applications (i.e., speakers), are used to tilt thismirror about its central axes. The electronically controlledtransducers convert currents to mechanical motion. The mir-ror is mounted in a holder that is attached to the surfacetransducers through steel wires. Elastic material, such asspring steel, bends according to the external force only, inde-pendent of its previous displacement (meaning it has nomemory), within its yield strength.14 Thus, transmission ofmovement is enabled by steel wires15 to minimize hysteresis.To tilt the mirror in both directions of a two-dimensionalplane, there are a total of four transducers in the setup, twofor each direction. A schematic for one direction of the galvois shown in Fig. 1(a). A current provided to the coil of thetransducer produces a magnetic dipole moment l.Depending upon the direction of this current, the coil withthe magnetic dipole moment is either attracted to or repelledfrom the magnet underneath it, resulting in mechanicalmovement of the stage, with the aid of the spring. Thecurrent-carrying coils of the two transducers meant for scan-ning one direction are connected in series, but with oppositepolarities. This geometry ensures that the movement stagesof the two transducers move equally, but in opposite direc-tions, thus doubling the symmetric travel range.

The current for each transducer’s coil is sourced from ahome-built circuit, which utilizes one high-current opera-tional-amplifier (op-amp) for each direction. The amplitudeand polarity of this controlling current I can be varied, inorder to scan the mirror across a range of angles in twodimensions. The circuit is controlled by a computer via amicro-controller board.

B. Setup

Figure 2 shows the galvo unit that we have constructed inour lab. The four surface transducers (SparkFun Electronics,COM-10975) are attached to a home-made vertical plate forease of use and assembly. All electrical connections are onthe other side of this vertical plate. Four custom-machinedaluminum arms are affixed to the movement stages of thetransducers, while steel wires (Malin Co., 0.020 Music wire)are attached to the other end of these arms. The steel wiressupport a home-machined mirror holder, which houses a12.7-mm diameter mirror (Edmund Optics, 83-483) in themiddle of the assembly, as shown in the figure. In our setup,the galvo mirror is positioned so that it turns the incomingbeam by a principal 90� plus a small scanning angle.16

Machine drawings of the galvo mirror holder, the mirror

mounting rods, the transducer mounting plate, and the galvoplate adapter are available as supplementary material.17

The control of the galvo is automated through a commer-cially available Arduino DUE microcontroller board (DUE).In addition to controlling the movement of the galvo mirror,the same microcontroller can synchronously collect the lightinformation and reconstruct the scanned image. This isaccomplished by arranging the detected light levels accord-ing to the controlled positions of the galvo mirror. Figure 3shows the schematic of the control path of our setup.Utilizing a microcontroller avoids having to communicatewith a computer through interfaces such as a universal serialbus (USB) or a general purpose interface bus (GPIB) at eachpoint, which could significantly limit the scan speed. A mini-mal Arduino code example (.ino) is provided17 for testingthe galvo scanning functionality.

Utilizing internal 12-bit digital-to-analog converters(DACs), the analog output pins of the DUE supply voltagesfrom approximately 0.5–2.5 V.18 In the absence of noise, thisDAC limits the scanning resolution of the galvo unit to onepart in 212 of the whole scan range. Following the ArduinoDAC output is a buffer op-amp (Analog Devices, OP482GPZ),

Fig. 1. Basic concept of the galvo system. (a) Simplified schematic of surface

transducers meant for scanning one direction is shown. The dashed rectangle

in this figure represents one such transducer, which consists of a movement

stage, current-carrying coil, an internal magnet, and a steel spring. The direc-

tion of the current and the magnetic moment thereof in the coil are shown.

(b) Schematic of the tilting of the mirror. The spacing between the steel wires

is 17.8 mm and the vertical travel range of the steel wire (maximum deflec-

tion of the transducer) is 70 lm (exaggerated in picture.)

69 Am. J. Phys., Vol. 85, No. 1, January 2017 Apparatus and Demonstration Notes 69

providing a protection layer between the sensitive DAC andthe high-current op-amp (Texas Instruments, OPA548). Thehigh-current op-amp amplifies the voltage output from theArduino to an appropriate level and supplies enough current todrive the transducers that convert these currents to mechanicalmovements. Note that the polarities of the transducers in series

are intentionally reversed to produce equal movement in oppo-site directions, so the mirror is tilted without displacement.

The user interface for controlling the galvo and data acqui-sition through the Arduino is implemented by an open-source Python-based instrument control system package,Pythics,19 and related libraries. Pythics is a completely open-source package, which makes it simple to customize andchange scanning parameters such as scan area, measurementtime at each point, step size, etc. The full circuit diagram isshown in the Appendix.

C. Bill of materials

The construction of the galvo mirror system is very cost-efficient, as can be seen by the following cost list of therequired parts:

(1) Arduino DUE microcontroller board: $49.99.(2) Transducers (SparkFun Electronics, COM-10975): $19.95

each, 4 required.(3) Mirror (Edmund Optics, 83-483): $16.(4) Power supply, þ15 and �15 V, (Acopian, TD15-100),

$270. However, much lower-cost power supplies can beused,21 for example, two Delta PMT-15V50W1AA,$23.45.

(5) Aluminum plate and other parts: �$15.(6) High-current op-amp OPA548 (Texas Instruments):

$14.87 each, 2 required.(7) Buffer op-amp OP482GPZ (Analog Devices): $5.83,

quad chip, but only two channels are used for bothdirections.

(8) Steel wire (Malin Co., 0.020 music wire): $3.53 for apackage of 100, but only one used.

Including some other basic electronics parts such as resis-tors, capacitors, wires, cables, and breadboards, the totalmaterial cost for the setup can be as low as $300, which issignificantly less than the cost of an off-the-shelf commercialgalvo unit.20

III. CHARACTERIZATION/SPECIFICATION

In this section, we characterize laser beam diameter, scanrange, noise, linearity, and scan speed of our galvo unit.

Fig. 2. (a) Front view of the galvo assembly, with mirror (12.7-mm diame-

ter) in the middle facing the camera. There are four cylindrical transducers

with the movement direction pointing into and out of the page. The BNC

connectors and cables shown on top left and right corners are for the electri-

cal connections. (b) Side view of the galvo assembly.

Fig. 3. Schematic of the mirror control and data acquisition of the galvo system.

70 Am. J. Phys., Vol. 85, No. 1, January 2017 Apparatus and Demonstration Notes 70

A. Mirror size

The mirror used in this setup is 12.7 mm in diameter.However, because the mirror surface is mounted at 45� fromthe incident and reflected beams, the effective cross-sectional area of the mirror is reduced by a factor of 1=

ffiffiffi2p

� 0:7. This reduction restricts the maximum beam diameterthat can be used in the system to �10 mm. Depending on theapplication requirements, such as beam diameter and scan-ning speed, a larger mirror (and thus increased inertia) canbe used at the expense of lower scanning speeds.

B. Angular scan range

The angular scan range of the galvo system depends on afew factors, such as its geometry, movement range of thetransducer, etc. In our setup, the maximum deflection of eachtransducer is �70 lm at its maximum current (rated at0.5 A). In this geometry, the two steel wires are �17:8 mmapart, leading to a nominal angular scan range of 0:45�.Experimentally, we observe a slightly larger scan range, asshown in Sec. III F.

The linear scan range of a complete optical setup dependson more than the angular scan range of the galvo unit; it isalso determined by physical factors, such as lens arrange-ment between the galvo and the specifications of the micro-scope objective (or the magnification).22

C. Noise

A simple optical setup is built around the galvo for thepurpose of noise characterization. A helium-neon gas laserwith wavelength k ¼ 632:8 nm (Research Electro-OpticsR-30989) is first attenuated by neutral density filters to avoidsaturating the camera sensor. The beam is then expanded byfive times to approximately 4 mm before being turned by aprincipal 90� off the galvo mirror. After the galvo, the beamis focused by a lens (300 mm) to a spot and is in turn imagedby a charge-coupled device (CCD) camera. After this focus-ing lens, the beam angle off the optical axis from the galvo isconverted to a displacement from the axis. Hence, a long-focal-distance lens is chosen so that the displacement is aslarge as possible, resulting in better accuracy.

With this system, the jitter of the imaged beam position isobserved to be about 0.5% of the total travel range, either atthe center or halfway toward the maximum travel range. Inother words, the jitter is about 20 out of the 212 control steps.Approximately 50% less noise is observed when a morestable DAC (e.g., AD5791) is used instead of the one onboard of an Arduino DUE, providing an alternative if lessjitter is desired.

D. Linearity

With the setup for the noise characterization, linearity ofthe galvo is also tested. Figure 4 shows superimposed imagesof the laser spots on different locations of the CCD, as dic-tated by preset scan control voltages spanning the wholescan range.

Clearly, the dots in this figure are aligned well in the verti-cal direction, while noticeable distortion can be seen at thecorners. With the imposed white lines as guides, one canestimate that the deviation from the horizontal lines areabout one dot, fairly uniformly across the vertical dimension.

While in this scan the dots are separated by 200 units in 212,the distortion, or non-linearity, is then 5% at the largest.

One possible source of this non-linearity is assembly errorand the hysteresis of the elastic material. However, it is pos-sible to correct for it by using an additional internal calibra-tion curve between the command output and the actual spotposition.

E. Symmetry of mirror movement

In order to check the axis of rotation of the mirror, themovement of each corner of the mirror holder is measured.Comparing the relevant pair responsible for the horizontaltilting (and likewise for the vertical), the symmetry of themovement can be determined. In an ideal setup, two sides ofthe mirror would always move the same distance in oppositedirections and hence the axis of rotation of the mirror wouldbe at the very center. Any asymmetry of the movementswould shift the axis of the mirror tilting. A linear variabledifferential transformer (Mahr, Millimar 1318) is used tomeasure the movement. In our galvo setup, the movement ofthe two corners for the vertical direction are 35.9 and41.2 lm, and 47.8 and 48.5 lm for the horizontal direction.These movements correspond to about 13% asymmetry inthe vertical tilting direction and about 1.5% difference in thehorizontal direction. Since the four transducers and armsshould be all symmetric, this deviation from the ideal situa-tion is likely due to assembly errors, such as lengths of theflexural wires at each arm, etc.

With these distances of movement and the size of themirror holder, the shift of the rotation axis of the mirror canbe calculated to be approximately 0.61 mm, which is smallcompared to the maximum beam diameter.

F. Frequency response

For the purpose of characterizing the frequency responseof this galvo, the control circuit is used to transmit dc or acvoltage control signals to the transducers. The full-swingscan angles with dc control signal are 0:67� and 0:46� for thex and y directions, respectively. These angles are slightlylarger than the expected 0:45� in either direction, the reasonfor which is speculated in Sec. IV. On providing ac controlsignals of varying frequency to the transducers, we observe aresponse as shown in Fig. 5.

Fig. 4. Superimposed spot images across the full scan range with step size of

200. White lines are guides for the eyes.

71 Am. J. Phys., Vol. 85, No. 1, January 2017 Apparatus and Demonstration Notes 71

As can be seen in Fig. 5, the experimental data are in rea-sonable agreement with the lineshapes for a driven dampedharmonic oscillator, as expected from a galvo unit such asours if driven with a constant ac current, as

h xð Þ ¼ Affiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2

0 � x2� �2 þ c2x2

q ; (1)

where hðxÞ is the scan angle, which depends on the drivingfrequency x, x0 is the resonant frequency, c is the linewidth, and the ratio A=x0 gives the amplitude of the low-frequency response. In practice, the deviation of the responsefrom the model is possibly due to the frequency-dependentimpedance of the transducer. As a result, the current throughthe transducer is not constant. The fitted resonant frequenciesare 343 and 351 Hz and the line widths are 46.0 and 34.6 Hzfor the x and y directions, respectively. The line width can beconverted to the quality factor Q using Q � x0=2c, givingthe Q-factor of 3.73 and 5.07 for the x and y directions,showing that the galvo unit acts as an underdamped drivenharmonic oscillator.

The frequency response data show a flat response up toabout 200 Hz for both directions. In this regime, the angular

scan range does not depend on the driving frequency.Therefore, according to this plot, the useful operating fre-quency range of this galvo is identified to be up to 200 Hz.This value sets a lower limit for the pixel dwell time. Forexample, using the full-scan range of 212 bits, the period(dwell time� 4096) should be longer than 1=ð200 HzÞ.Therefore, the pixel dwell time should be longer than1.22 ls.

IV. APPLICATION—CONFOCAL SCANNING

OF PHOTOLUMINESCENCE FROM DIAMOND

NANOCRYSTALS

One application for which we make use of the galvo sys-tem is CLSM of photoluminescence (PL) of diamond nano-crystals. We have built this setup as a part of optical systemsthat are used to detect the presence of nitrogen-vacancy(NV) centers in the diamond nanocrystals, and further studythe interaction of these NV centers with magnetic fields.23

With other essential elements, such as an excitation laser, aphoton-counting module, a microscope objective, an opticalfiber, and the PL from diamond nanocrystals can be detected.If the objective (numerical aperture 0.9) and the PL collec-tion lens in our setup give diffraction limited spots, the spa-tial resolution can be sub-micron using the presented galvosystem.

Figure 6 illustrates the optical setup used for diamondnanocrystal PL detection. A fiber-coupled laser from a diodeis collimated with a lens, and then combined into the mainbeam path via a dichroic mirror. The laser beam onto thegalvo is imaged onto the back of the objective by a pair ofrelay lenses, and then focused onto the sample. The returningPL light is collected by the objective, reflected off the galvo,and then focused onto the detection fiber leading to thedetector.

Since the sample is illuminated in the laser focusing cone,any point of the sample in that cone can emit PL. Therefore,in a confocal microscopy setup, a confocal pinhole is neededto spatially filter the out-of-focus PL. The detection fiber thatis used to collect the PL to the detector acts as a confocalpinhole.24,25 Using optical fibers as confocal pinholes hasseveral advantages, including ease of alignment, ease ofcleaning,24 and the fact that a single mode fiber has a fieldmode diameter of only a few microns and guides only onefield mode.26

Fig. 5. Frequency response of the galvo in terms of its scan angle. Note that

it closely resembles the lineshapes of a driven damped harmonic oscillator,

as seen by the fit.

Fig. 6. Optical system for confocal scanning for photoluminesence.

72 Am. J. Phys., Vol. 85, No. 1, January 2017 Apparatus and Demonstration Notes 72

As was briefly discussed in Sec. III B, the linear scanrange on a sample is determined by both the galvo unit andother optical elements in the setup. Figure 7 illustrates howthe galvo angular scan range translates to the linear scanrange on the sample surface in our setup. An introductionand detailed analysis of this kind of standard confocal scan-ning setup can be found in other texts.12 Here, only the rele-vant parts are explained.

The scan lens and tube lens between the galvo and theobjective (together also called the relay lenses) in Fig. 7accomplish two purposes: (i) to image the beam at the galvoto the back of the objective and vice versa, and (ii) toexpand/shrink the beam diameter by the ratio of the focallengths, d3=d2 ¼ f3=f2. To achieve these purposes, the galvois physically placed a distance f3 away from the scan lensand the objective is placed distance f2 away from the tubelens while the distance between the lenses is f3 þ f2. Supposea collimated light beam enters the scan lens at a galvo tiltangle by0 . For a light beam passing through the focal point of

the scan lens, the chief ray between the scan lens and thetube lens is displaced but still parallel to the optical axis. Thedisplacement of the chief ray is derived by Dx0 ¼ f3 tanðby0 Þ.This same displacement of the chief ray entering the tubelens provides the angle at which the beam enters the objec-tive, Dx0 ¼ f2 tanðbyÞ. Hence, by ¼ arctan½ðf3=f2Þ tan by0 �, or

in the small angle limit, simply by � ðf3=f2Þby0 . On the other

side of the objective with focal length f1 (represented by asingle lens in Fig. 7),22 the light is focused onto the sample.The displacement from the optical axis, Dx ¼ f1 tan hb,defines half of the scan range on the sample. This provides arelationship between the scan range on the sample and thegalvo tilt angle of

Scan range ¼ 2f1

f3

f2

� �tan by0 : (2)

For example, the relay lenses that we used for this applica-tion had f3 ¼ 200 mm and f2 ¼ 300 mm, and the objectivehad a focal length of 1.8 mm. Using our equations above, anominal scan range of �10 lm is expected. This is in goodagreement with the experimentally achieved scan range, asshown in Fig. 8(b), of about 14 lm. The slight differencebetween the observed and calculated values of scan rangeand scan angles of the galvo (as in Sec. III F) might bebecause of unaccounted flexing of the steel wires, causingextra tilting of the mirror, or miscalibration of the transducermovement.

Figure 8 shows typical images obtained using our opticalsystem with the galvo. Figure 8(a) shows the PL count rate

from scanning across an area of a flat piece of silicon waferwith scattered diamond nanocrystals. The bright-field micro-scope image of the same scan area is shown in Fig. 8(b). Thehigh-count spots in Fig. 8(b) suggest PL source in Fig. 8(a),demonstrating the ability of our optical setup to detect PLsources, such as NV centers in diamond nanocrystals.

V. SUMMARY

We present a home-built mirror galvanometer system thatis robust and very cost-efficient. Characterizations of itsessential properties are also presented. A simple and usefulapplication of the unit is highlighted. We conclude that thiseasy-to-build, simple, robust, and economical galvo unit issuitable for optical setups in intermediate and advancedundergraduate level laboratories.

ACKNOWLEDGMENTS

The authors thank Elliot Jenner of University ofPittsburgh and Tanya Malhotra of University of Rochesterfor giving helpful feedback on a draft of this manuscript.

APPENDIX: DIAGRAM FOR THE CONTROL

CIRCUIT

Here, we present the control circuit diagram (see Fig. 9)for driving the galvo system and a few notes.

Fig. 7. Schematic diagram of the light traces from galvo to the objective:

f3;2;1 are the focal lengths of the scan lens, tube lens, and objective, respec-

tively; by0 and by are the angles entering and exiting the scan and tube lenses

pair; d3;2 are the beam diameters.

Fig. 8. PL scan image. (a) Spatial scan of photon count rate; this image is

obtained with a step size of 0.17 lm and a pixel dwell time of 50 ms. (b) The

bright-field image of the scanned area; the length of the scale bar is 2 lm.

73 Am. J. Phys., Vol. 85, No. 1, January 2017 Apparatus and Demonstration Notes 73

(1) The purpose of the ISL21080CIH315Z-TK (Intersil)1.5 V voltage reference and the 1 and 13-kX resistors isto achieve a level shifting from 0 to 3.3 V (Arduino out-put) to 615 V.

(2) The purpose of the 20-X power resistor is to dissipatemost of the power output and also make the load moreresistive rather than inductive.

(3) The combination of the 13-kX resistor and the 0.1-lFcapacitor in parallel forms a RC filter with time constantabout 1.3 ms. This filter helps in stabilizing the output,but is still fast enough so as not to slow down theresponse of the galvo.

Consider the vectors of the ray of incidence ~i, the ray ofreflection ~r , and the normal vector n̂ to the mirror surface inone plane, as shown in Fig. 10(a). Since only the directionsare relevant, we assume these vectors have unit length andplace them in a spherical coordinate system with the azimuthplane in page where h ¼ p=2. When the mirror is tilted hori-zontally (vertically), n̂ is moved in the / (h) direction. Thelaw of reflection allows us to write down the relationshipbetween them as

~r þ ð�~i Þ ¼ 2½ð�~i Þ n̂�n̂: (A1)

In the first and simpler case, the mirror is tilted only in theazimuthal direction. All three vectors are therefore in the azi-muth plane. If the mirror is tilted by a scan angle hs=2 in the/ direction, the reflected ray~r is deviated by hs, as illustratedin Fig. 10(b). This is the scan angle range for the horizontaldirection.

In the second case, the mirror is tilted by hs=2 in the hdirection. The three vectors are set up in the spherical coordi-nates as, in the usual ðr; h;/Þ notation,

~i ¼ 1;p2; p

� �; n̂ ¼ 1;

p2� hs

2;p4

� �; and

~r ¼ 1;p2� hv;/v

� �: (A2)

Here, hv is the quantity in pursuit, the angle of the reflected raydeviated from the azimuth plane. The vector~r can now be cal-culated using Eq. (A1). One way to perform the scalar product

and vector subtraction is to convert to Cartesian coordinates.

Hence, ð�~i Þ n̂¼� ixnxþ iynyþ iznzð Þ¼sin p=2�hs=2ð Þ1=ffiffiffi2p

¼cos hs=2ð Þ1=ffiffiffi2p

; rx¼2½ð�~i Þ n̂�nxþ ix¼2 cos hs=2ð Þ1=ffiffiffi2p

cos hs=2ð Þ1=ffiffiffi2p�1¼cos2 hs=2ð Þ�1; ry¼cos2 hs=2ð Þ, and

rz¼ 2cos hs=2ð Þ1=ffiffiffi2p

sin hs=2ð Þ¼ sinhs=ffiffiffi2p

. Converting back

to spherical coordinates, rh¼ cos�1ðz=rrÞ, where rr¼1.

Fig. 9. Complete circuit diagram for driving the galvo system (OP1: Texas Instruments OPA548, OP2: Analog Devices OP482GPZ, V: Intersil

ISL21080CIH315Z-TK 1.5 V voltage reference, C: 0.1 lF ceramic, and C1: 1.6 nF ceramic).

Fig. 10. (a) The relationship between ray of incidence ~i, normal vector of

the mirror n̂, and the ray of reflection ~r . (b) The three vectors in the azi-

muthal plane when the mirror is tilted only in the / (horizontal) direction.

74 Am. J. Phys., Vol. 85, No. 1, January 2017 Apparatus and Demonstration Notes 74

Therefore, rh¼ cos�1ðsinhs=ffiffiffi2pÞ. For hs much smaller than 1,

sinhs� hs, so rh� cos�1ðhs=ffiffiffi2pÞ. Again for small hs, expand-

ing rh at 0 gives, to first order, rh�p=2�hs=ffiffiffi2p

. Comparing

with Eq. (A2), we find the desired quantity hv¼ hs=ffiffiffi2p

.Finally, comparing the above two cases, for the same amountof tilting of the mirror, we found that the scan range in the ver-

tical direction is reduced by a factor offfiffiffi2p

, due to the geomet-rical arrangement of the mirror.

a)Electronic mail: jeh114@pitt.edub)Electronic mail: dursobr@pitt.edu1F. Spitzer and B. Howarth, Principles of Modern Instrumentation (Holt,

Rinehart and Winston, 1972).2For example, Zero galvanometer by Chauvin Arnoux.3R. P. Aylward, “Advances and technologies of galvanometer-based optical

scanners,” Proc. SPIE 3787, 158 (1999).4M. D. Mccarty, U.S. patent 2,351,353 (13 June 1944).5J. S. Chandler, D. M. Orlicki, and J. M. Kresock, U.S. patent 5,280,377

(18 January 1994).6A. Gh. Podoleanu, G. M. Dobre, and D. A. Jackson, “En-face coherence

imaging using galvanometer scanner modulation,” Opt. Lett. 23(3),

147–149 (1998).7Tailored Light 2—Laser Application Technology, edited by R. Poprawe

(Springer-Verlag, Heidelberg, 2011).8D. Perrottet et al., “Using Lasers to Dice Thin Silicon Wafers,” Adv.

Packag. 17, 35–37 (2008).9R. A. Ganeev, Laser—Surface Interactions (Springer Science & Business

Media, Dordrecht, 2014).10C. J. R. Sheppard and D. M. Shotton, Confocal Laser Scanning

Microscopy (Springer-Verlag, Singapore, 1997).11S. Inou�e, in Handbook of Biological Confocal Microscopy, 3rd ed., edited by J.

B. Pawley (Springer Science & Business Media, Dordrecht, 2006), pp. 1–16.12For example, E. H. K. Stelzer, in Handbook of Biological Confocal

Microscopy, 3rd ed., edited by J. B. Pawley (Springer Science & Business

Media, Dordrecht, 2006), pp. 208–220.13The manual for Galvo system GVS012 from Thorlabs, <http://www.thor-

labs.com/thorcat/20300/GVS012_M-Manual.pdf>.14M. F. Ashby, H. Shercliff, and D. Cebon, Materials: Engineering, Science,

Processing and Design, 3rd ed. (Butterworth-Heinemann, Oxford, 2013), p. 4.15J. E. Shigley and C. R. Mischke, Mechanical Engineering Design, 5th ed.

(McGraw-Hill, New York, 1989).

16Since the mirror is placed 45� relative to the horizontal incident beam, for

small scan angles the deflection of the reflected beam in the vertical direc-

tion is reduced by a factor offfiffiffi2p

, while the scan angle in the horizontal

direction is not affected. The result of this effect is that the field of view

has an aspect ratio offfiffiffi2p

: 1.17See supplementary material at http://dx.doi.org/10.1119/1.4972046 for

machine drawings and sample codes.18Technical datasheet for the Atmel processor SAM3X8E used in Arduino

DUEs, <http://www.atmel.com/Images/Atmel-11057-32-bit-Cortex-M3-

Microcontroller-SAM3X-SAM3A_Datasheet.pdf>.19Pythics Project, <https://github.com/dursobr/pythics>.20The authors do not intend to make an impression that the presented design

is comparable or superior to the commercially-available units in its charac-

terized performance. This is a simple, inexpensive, and robust alternative

for those applications where our presented characteristics meet the criteria.21Important requirements for this application are output voltages (615 V)

and the current limit. This application draws a maximum of about 2 � 15

V/30 X � 1 A. The noise from the power supply has little effect on the

performance of the galvo.22For an infinity-corrected microscope objective, there must be a second

lens for the collimated light from the focal point of the objective to focus

again to form an image. Only then is the magnification meaningful.

Objective manufacturers specify the magnification M assuming a second

lens, with a focal length F. This focal length is called the tube lens focal

length or the reference focal length. When building a customized micros-

copy system around an objective, it can be modeled by a simple lens with

focal length f for calculating the magnification, where f can be derived by

f ¼ F=M. Unfortunately, the reference focal length is not standardized

across manufacturers. For example, Olympus uses 180 mm while

Mitutoyo uses 200 mm. See R. Juskaitis, in Handbook of BiologicalConfocal Microscopy, 3rd ed., edited by J. B. Pawley (Springer Science &

Business Media, Dordrecht, 2006), pp. 239–250.23K. Iakoubovskii, G. J. Adriaenssens, and M. Nesladek, “Photochromism of

vacancy-related centres in diamond,” J. Phys.: Condens. Matter 12,

189–199 (2000).24T. Dabbs and M. Glass, “Single-mode fibres used as confocal microscope

pinholes,” Appl. Opt. 31(6), 705–706 (1992).25P. Delaney and M. Harris, in Handbook of Biological Confocal

Microscopy, 3rd ed., edited by J. B. Pawley (Springer Science & Business

Media, Dordrecht, 2006), pp. 501–515.26J. Hecht, Understanding Fiber Optics, 3rd ed. (Prentice Hall, Upper

Saddle River, NJ, 1999).

75 Am. J. Phys., Vol. 85, No. 1, January 2017 Apparatus and Demonstration Notes 75