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

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1 APPARATUS AND DEMONSTRATION NOTES The downloaded PDF for any Note in this section contains all the Notes in this section. John Essick, Editor Deartment of Physics, Reed College, Portland, OR 970 This deartment welcomes brief communications reorting new demonstrations, laboratory equiment, techniques, or materials of interest to teachers of hysics. Notes on new alications of older aaratus, measurements sulementing data sulied by manufacturers, information which, while not new, is not generally known, rocurement information, and news about aaratus under develoment may be suitable for ublication in this section. Neither the American Journal of Physics nor the Editors assume resonsibility for the correctness of the information resented. Manuscrits should be submitted using the web-based system that can be accessed via the American Journal of Physics home age, htt://aj.dickinson.edu and will be forwarded to the ADN editor for consideration. Design and construction of a cost-efficient Arduino-based mirror galvanometer system for scanning otical microscoy Jen-Feng Hsu, a) Shonali Dhingra, and Brian D Urso b) Deartment of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 1560 (Received 19 November 014; acceted 15 November 016) Mirror galvanometer systems (galvos) are commonly emloyed in research and commercial alications in areas involving laser imaging, laser machining, laser-light shows, and others. Here, we resent a robust, moderate-seed, and cost-efficient home-built galvo system. The mechanical art of this design consists of one mirror, which is tilted around two axes with multile surface transducers. We demonstrate the ability of this galvo by scanning the mirror using a comuter, via a custom driver circuit. The erformance of the galvo, including scan range, noise, linearity, and scan seed, is characterized. As an alication, we show that this galvo system can be used in a confocal scanning microscoy system. VC 017 American Association of Physics Teachers. [htt://dx.doi.org/ / ] I. INTRODUCTION A galvanometer is a sensitive electromechanical actuator that is used to detect feeble electrical currents on the order of microams. 1, It works on the rincile of a current-carrying coil exeriencing a torque when laced in an external magnetic field, due to its effective magnetic diole moment l. A mechanical ointer, which is a art of the coil, moves over a scale in resonse to the resence of an electrical current, roving a visible resonse. In lace of a ointer, a galvo uses a laser beam reflected off a movable mirror. Galvo systems are widely used in otical setus that require recision control, such as in ositioning and scanning of laser beams. Galvo systems find extensive use in various scientific and non-scientific equiment used for rocesses such as laser imaging, laser machining, laser welding, laser ablation, laser cleaning, wafer dicing, laser-light shows, etc. 3 9 One common use for a galvo system is in confocal laser scanning microscoy (CLSM). This technique is used to obtain high-resolution otical images of toologically comlex objects by rastering a laser beam over individual twodimensional surfaces of the object at different deths, and collecting only the in-focus scattered or hotoluminescent light. 10,11 The most common commercial imlementation of the two-dimensional rastering is the two-closely-sacedscan-mirrors arrangement, 1 in which two mirrors are tilted in orthogonal directions. A tyical commercial galvo system (for examle, Thorlabs GVS01) has features such as low drift and recise osition control. These features are achieved by a servo motor control system instead of a single magnet and a coil as originally develoed. The servo systems are closed-loo systems, so the motor ositions are internally measured and fed back to calculate the errors, which are in turn corrected by further adjusting the motor. It has a full swing angle of u to 60 (deending on the beam diameter) and a smaller swing of 60: for a fast (1 khz)scan. 13 The cost for such a commercial unit could be $500 or more. Thus, building a microscoe system around such a unit could lead to substantially high costs, often not feasible for use in educational laboratories. Furthermore, the comlex osition sensor system used by the servo controller requires recise internal alignment, making reair and maintenance exensive. Due to these reasons, a simle, robust, and inexensive galvo system could be very useful. Here, we resent such an affordable alternative to a commercial galvo unit, which has a robust and accessible design, making it easy to reair and maintain. It is an oen-loo system, as oosed to a closed-loo system as in a tyical commercial unit, meaning there is no internal measurement and feedback of the galvo mirror osition. Thus, this galvo may be subject to more drift and osition error. Because of its simlicity, building such a galvanometer system can be a great educational exercise in intermediate and advanced undergraduate level courses, requiring only basic mechanics, electronics, and rogramming skills and techniques. 68 Am. J. Phys. 85 (1), January 017 htt://aat.org/aj VC 017 American Association of Physics Teachers 68

2 We describe the concet and setu of the galvo system in Sec. II. Characterizations of some of its roerties, such as the mirror size, scan range, noise, linearity, center of rotation, and frequency resonse, are reorted in Sec. III. Finally, we resent an alication of this galvo system confocal scanning microscoy which is erformed in conjunction with other otical elements such as lasers, lenses, otical fibers, and microscoe objective, in Sec. IV. II. DESIGN AND CONSTRUCTION OF THE GALVO A. Basic concet For simlicity, the galvo system resented here uses one mirror, as oosed to two used in many commercial models. Surface transducers, which are originally designed for audio transduction alications (i.e., seakers), are used to tilt this mirror about its central axes. The electronically controlled transducers convert currents to mechanical motion. The mirror is mounted in a holder that is attached to the surface transducers through steel wires. Elastic material, such as sring steel, bends according to the external force only, indeendent of its revious dislacement (meaning it has no memory), within its yield strength. 14 Thus, transmission of movement is enabled by steel wires 15 to minimize hysteresis. To tilt the mirror in both directions of a two-dimensional lane, there are a total of four transducers in the setu, two for each direction. A schematic for one direction of the galvo is shown in Fig. 1(a). A current rovided to the coil of the transducer roduces a magnetic diole moment l. Deending uon the direction of this current, the coil with the magnetic diole moment is either attracted to or reelled from the magnet underneath it, resulting in mechanical movement of the stage, with the aid of the sring. The current-carrying coils of the two transducers meant for scanning one direction are connected in series, but with oosite olarities. This geometry ensures that the movement stages of the two transducers move equally, but in oosite directions, thus doubling the symmetric travel range. The current for each transducer s coil is sourced from a home-built circuit, which utilizes one high-current oerational-amlifier (o-am) for each direction. The amlitude and olarity of this controlling current I can be varied, in order to scan the mirror across a range of angles in two dimensions. The circuit is controlled by a comuter via a micro-controller board. B. Setu Figure shows the galvo unit that we have constructed in our lab. The four surface transducers (SarkFun Electronics, COM-10975) are attached to a home-made vertical late for ease of use and assembly. All electrical connections are on the other side of this vertical late. Four custom-machined aluminum arms are affixed to the movement stages of the transducers, while steel wires (Malin Co., 0.00 Music wire) are attached to the other end of these arms. The steel wires suort a home-machined mirror holder, which houses a 1.7-mm diameter mirror (Edmund Otics, ) in the middle of the assembly, as shown in the figure. In our setu, the galvo mirror is ositioned so that it turns the incoming beam by a rincial 90 lus a small scanning angle. 16 Machine drawings of the galvo mirror holder, the mirror Fig. 1. Basic concet of the galvo system. (a) Simlified schematic of surface transducers meant for scanning one direction is shown. The dashed rectangle in this figure reresents one such transducer, which consists of a movement stage, current-carrying coil, an internal magnet, and a steel sring. The direction of the current and the magnetic moment thereof in the coil are shown. (b) Schematic of the tilting of the mirror. The sacing between the steel wires is 17.8 mm and the vertical travel range of the steel wire (maximum deflection of the transducer) is 70 lm (exaggerated in icture.) mounting rods, the transducer mounting late, and the galvo late adater are available as sulementary material. 17 The control of the galvo is automated through a commercially available Arduino DUE microcontroller board (DUE). In addition to controlling the movement of the galvo mirror, the same microcontroller can synchronously collect the light information and reconstruct the scanned image. This is accomlished by arranging the detected light levels according to the controlled ositions of the galvo mirror. Figure 3 shows the schematic of the control ath of our setu. Utilizing a microcontroller avoids having to communicate with a comuter through interfaces such as a universal serial bus (USB) or a general urose interface bus (GPIB) at each oint, which could significantly limit the scan seed. A minimal Arduino code examle (.ino) is rovided 17 for testing the galvo scanning functionality. Utilizing internal 1-bit digital-to-analog converters (DACs), the analog outut ins of the DUE suly voltages from aroximately V. 18 In the absence of noise, this DAC limits the scanning resolution of the galvo unit to one art in 1 of the whole scan range. Following the Arduino DAC outut is a buffer o-am (Analog Devices, OP48GPZ), 69 Am. J. Phys., Vol. 85, No. 1, January 017 Aaratus and Demonstration Notes 69

3 are intentionally reversed to roduce equal movement in oosite directions, so the mirror is tilted without dislacement. The user interface for controlling the galvo and data acquisition through the Arduino is imlemented by an oensource Python-based instrument control system ackage, Pythics, 19 and related libraries. Pythics is a comletely oensource ackage, which makes it simle to customize and change scanning arameters such as scan area, measurement time at each oint, ste size, etc. The full circuit diagram is shown in the Aendix. Fig.. (a) Front view of the galvo assembly, with mirror (1.7-mm diameter) in the middle facing the camera. There are four cylindrical transducers with the movement direction ointing into and out of the age. The BNC connectors and cables shown on to left and right corners are for the electrical connections. (b) Side view of the galvo assembly. roviding a rotection layer between the sensitive DAC and the high-current o-am (Texas Instruments, OPA548). The high-current o-am amlifies the voltage outut from the Arduino to an aroriate level and sulies enough current to drive the transducers that convert these currents to mechanical movements. Note that the olarities of the transducers in series C. Bill of materials The construction of the galvo mirror system is very costefficient, as can be seen by the following cost list of the required arts: (1) Arduino DUE microcontroller board: $ () Transducers (SarkFun Electronics, COM-10975): $19.95 each, 4 required. (3) Mirror (Edmund Otics, ): $16. (4) Power suly, þ15 and 15 V, (Acoian, TD15-100), $70. However, much lower-cost ower sulies can be used, 1 for examle, two Delta PMT-15V50W1AA, $3.45. (5) Aluminum late and other arts: $15. (6) High-current o-am OPA548 (Texas Instruments): $14.87 each, required. (7) Buffer o-am OP48GPZ (Analog Devices): $5.83, quad chi, but only two channels are used for both directions. (8) Steel wire (Malin Co., 0.00 music wire): $3.53 for a ackage of 100, but only one used. Including some other basic electronics arts such as resistors, caacitors, wires, cables, and breadboards, the total material cost for the setu can be as low as $300, which is significantly less than the cost of an off-the-shelf commercial galvo unit. 0 III. CHARACTERIZATION/SPECIFICATION In this section, we characterize laser beam diameter, scan range, noise, linearity, and scan seed of our galvo unit. Fig. 3. Schematic of the mirror control and data acquisition of the galvo system. 70 Am. J. Phys., Vol. 85, No. 1, January 017 Aaratus and Demonstration Notes 70

4 A. Mirror size The mirror used in this setu is 1.7 mm in diameter. However, because the mirror surface is mounted at 45 from the incident and reflected beams, the effective crosssectional area of the mirror is reduced by a factor of 1= ffiffi 0:7. This reduction restricts the maximum beam diameter that can be used in the system to 10 mm. Deending on the alication requirements, such as beam diameter and scanning seed, a larger mirror (and thus increased inertia) can be used at the exense of lower scanning seeds. B. Angular scan range The angular scan range of the galvo system deends on a few factors, such as its geometry, movement range of the transducer, etc. In our setu, the maximum deflection of each transducer is 70 lm at its maximum current (rated at 0.5 A). In this geometry, the two steel wires are 17:8 mm aart, leading to a nominal angular scan range of 0:45. Exerimentally, we observe a slightly larger scan range, as shown in Sec. III F. The linear scan range of a comlete otical setu deends on more than the angular scan range of the galvo unit; it is also determined by hysical factors, such as lens arrangement between the galvo and the secifications of the microscoe objective (or the magnification). C. Noise A simle otical setu is built around the galvo for the urose of noise characterization. A helium-neon gas laser with wavelength k ¼ 63:8 nm (Research Electro-Otics R-30989) is first attenuated by neutral density filters to avoid saturating the camera sensor. The beam is then exanded by five times to aroximately 4 mm before being turned by a rincial 90 off the galvo mirror. After the galvo, the beam is focused by a lens (300 mm) to a sot and is in turn imaged by a charge-couled device (CCD) camera. After this focusing lens, the beam angle off the otical axis from the galvo is converted to a dislacement from the axis. Hence, a longfocal-distance lens is chosen so that the dislacement is as large as ossible, resulting in better accuracy. With this system, the jitter of the imaged beam osition is observed to be about 0.5% of the total travel range, either at the center or halfway toward the maximum travel range. In other words, the jitter is about 0 out of the 1 control stes. Aroximately 50% less noise is observed when a more stable DAC (e.g., AD5791) is used instead of the one on board of an Arduino DUE, roviding an alternative if less jitter is desired. D. Linearity With the setu for the noise characterization, linearity of the galvo is also tested. Figure 4 shows suerimosed images of the laser sots on different locations of the CCD, as dictated by reset scan control voltages sanning the whole scan range. Clearly, the dots in this figure are aligned well in the vertical direction, while noticeable distortion can be seen at the corners. With the imosed white lines as guides, one can estimate that the deviation from the horizontal lines are about one dot, fairly uniformly across the vertical dimension. Fig. 4. Suerimosed sot images across the full scan range with ste size of 00. White lines are guides for the eyes. While in this scan the dots are searated by 00 units in 1, the distortion, or non-linearity, is then 5% at the largest. One ossible source of this non-linearity is assembly error and the hysteresis of the elastic material. However, it is ossible to correct for it by using an additional internal calibration curve between the command outut and the actual sot osition. E. Symmetry of mirror movement In order to check the axis of rotation of the mirror, the movement of each corner of the mirror holder is measured. Comaring the relevant air resonsible for the horizontal tilting (and likewise for the vertical), the symmetry of the movement can be determined. In an ideal setu, two sides of the mirror would always move the same distance in oosite directions and hence the axis of rotation of the mirror would be at the very center. Any asymmetry of the movements would shift the axis of the mirror tilting. A linear variable differential transformer (Mahr, Millimar 1318) is used to measure the movement. In our galvo setu, the movement of the two corners for the vertical direction are 35.9 and 41. lm, and 47.8 and 48.5 lm for the horizontal direction. These movements corresond to about 13% asymmetry in the vertical tilting direction and about 1.5% difference in the horizontal direction. Since the four transducers and arms should be all symmetric, this deviation from the ideal situation is likely due to assembly errors, such as lengths of the flexural wires at each arm, etc. With these distances of movement and the size of the mirror holder, the shift of the rotation axis of the mirror can be calculated to be aroximately 0.61 mm, which is small comared to the maximum beam diameter. F. Frequency resonse For the urose of characterizing the frequency resonse of this galvo, the control circuit is used to transmit dc or ac voltage control signals to the transducers. The full-swing scan angles with dc control signal are 0:67 and 0:46 for the x and y directions, resectively. These angles are slightly larger than the exected 0:45 in either direction, the reason for which is seculated in Sec. IV. On roviding ac control signals of varying frequency to the transducers, we observe a resonse as shown in Fig Am. J. 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5 scan range does not deend on the driving frequency. Therefore, according to this lot, the useful oerating frequency range of this galvo is identified to be u to 00 Hz. This value sets a lower limit for the ixel dwell time. For examle, using the full-scan range of 1 bits, the eriod (dwell time 4096) should be longer than 1=ð00 HzÞ. Therefore, the ixel dwell time should be longer than 1. ls. Fig. 5. Frequency resonse of the galvo in terms of its scan angle. Note that it closely resembles the lineshaes of a driven damed harmonic oscillator, as seen by the fit. As can be seen in Fig. 5, the exerimental data are in reasonable agreement with the lineshaes for a driven damed harmonic oscillator, as exected from a galvo unit such as ours if driven with a constant ac current, as hx ð Þ ¼ A q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; (1) þ c x x 0 x where hðxþ is the scan angle, which deends on the driving frequency x, x 0 is the resonant frequency, c is the line width, and the ratio A=x 0 gives the amlitude of the lowfrequency resonse. In ractice, the deviation of the resonse from the model is ossibly due to the frequency-deendent imedance of the transducer. As a result, the current through the transducer is not constant. The fitted resonant frequencies are 343 and 351 Hz and the line widths are 46.0 and 34.6 Hz for the x and y directions, resectively. The line width can be converted to the quality factor Q using Q x 0 =c, giving the Q-factor of 3.73 and 5.07 for the x and y directions, showing that the galvo unit acts as an underdamed driven harmonic oscillator. The frequency resonse data show a flat resonse u to about 00 Hz for both directions. In this regime, the angular IV. APPLICATION CONFOCAL SCANNING OF PHOTOLUMINESCENCE FROM DIAMOND NANOCRYSTALS One alication for which we make use of the galvo system is CLSM of hotoluminescence (PL) of diamond nanocrystals. We have built this setu as a art of otical systems that are used to detect the resence of nitrogen-vacancy (NV) centers in the diamond nanocrystals, and further study the interaction of these NV centers with magnetic fields. 3 With other essential elements, such as an excitation laser, a hoton-counting module, a microscoe objective, an otical fiber, and the PL from diamond nanocrystals can be detected. If the objective (numerical aerture 0.9) and the PL collection lens in our setu give diffraction limited sots, the satial resolution can be sub-micron using the resented galvo system. Figure 6 illustrates the otical setu used for diamond nanocrystal PL detection. A fiber-couled laser from a diode is collimated with a lens, and then combined into the main beam ath via a dichroic mirror. The laser beam onto the galvo is imaged onto the back of the objective by a air of relay lenses, and then focused onto the samle. The returning PL light is collected by the objective, reflected off the galvo, and then focused onto the detection fiber leading to the detector. Since the samle is illuminated in the laser focusing cone, any oint of the samle in that cone can emit PL. Therefore, in a confocal microscoy setu, a confocal inhole is needed to satially filter the out-of-focus PL. The detection fiber that is used to collect the PL to the detector acts as a confocal inhole. 4,5 Using otical fibers as confocal inholes has several advantages, including ease of alignment, ease of cleaning, 4 and the fact that a single mode fiber has a field mode diameter of only a few microns and guides only one field mode. 6 Fig. 6. Otical system for confocal scanning for hotoluminesence. 7 Am. J. Phys., Vol. 85, No. 1, January 017 Aaratus and Demonstration Notes 7

6 As was briefly discussed in Sec. III B, the linear scan range on a samle is determined by both the galvo unit and other otical elements in the setu. Figure 7 illustrates how the galvo angular scan range translates to the linear scan range on the samle surface in our setu. An introduction and detailed analysis of this kind of standard confocal scanning setu can be found in other texts. 1 Here, only the relevant arts are exlained. The scan lens and tube lens between the galvo and the objective (together also called the relay lenses) in Fig. 7 accomlish two uroses: (i) to image the beam at the galvo to the back of the objective and vice versa, and (ii) to exand/shrink the beam diameter by the ratio of the focal lengths, d 3 =d ¼ f 3 =f. To achieve these uroses, the galvo is hysically laced a distance f 3 away from the scan lens and the objective is laced distance f away from the tube lens while the distance between the lenses is f 3 þ f. Suose a collimated light beam enters the scan lens at a galvo tilt angle b y 0. For a light beam assing through the focal oint of the scan lens, the chief ray between the scan lens and the tube lens is dislaced but still arallel to the otical axis. The dislacement of the chief ray is derived by Dx 0 ¼ f 3 tanðb y 0Þ. This same dislacement of the chief ray entering the tube lens rovides the angle at which the beam enters the objective, Dx 0 ¼ f tanðb y Þ. Hence, b y ¼ arctan½ðf 3 =f Þ tan b y 0Š, or in the small angle limit, simly b y ðf 3 =f Þb y 0. On the other side of the objective with focal length f 1 (reresented by a single lens in Fig. 7), the light is focused onto the samle. The dislacement from the otical axis, Dx ¼ f 1 tan h b, defines half of the scan range on the samle. This rovides a relationshi between the scan range on the samle and the galvo tilt angle of f 3 Scan range ¼ f 1 tan b f y 0: () For examle, the relay lenses that we used for this alication had f 3 ¼ 00 mm and f ¼ 300 mm, and the objective had a focal length of 1.8 mm. Using our equations above, a nominal scan range of 10 lm is exected. This is in good agreement with the exerimentally achieved scan range, as shown in Fig. 8(b), of about 14 lm. The slight difference between the observed and calculated values of scan range and scan angles of the galvo (as in Sec. III F) might be because of unaccounted flexing of the steel wires, causing extra tilting of the mirror, or miscalibration of the transducer movement. Figure 8 shows tyical images obtained using our otical system with the galvo. Figure 8(a) shows the PL count rate Fig. 8. PL scan image. (a) Satial scan of hoton count rate; this image is obtained with a ste size of 0.17 lm and a ixel dwell time of 50 ms. (b) The bright-field image of the scanned area; the length of the scale bar is lm. from scanning across an area of a flat iece of silicon wafer with scattered diamond nanocrystals. The bright-field microscoe image of the same scan area is shown in Fig. 8(b). The high-count sots in Fig. 8(b) suggest PL source in Fig. 8(a), demonstrating the ability of our otical setu to detect PL sources, such as NV centers in diamond nanocrystals. V. SUMMARY We resent a home-built mirror galvanometer system that is robust and very cost-efficient. Characterizations of its essential roerties are also resented. A simle and useful alication of the unit is highlighted. We conclude that this easy-to-build, simle, robust, and economical galvo unit is suitable for otical setus in intermediate and advanced undergraduate level laboratories. ACKNOWLEDGMENTS The authors thank Elliot Jenner of University of Pittsburgh and Tanya Malhotra of University of Rochester for giving helful feedback on a draft of this manuscrit. Fig. 7. Schematic diagram of the light traces from galvo to the objective: f 3;;1 are the focal lengths of the scan lens, tube lens, and objective, resectively; b y 0 and b y are the angles entering and exiting the scan and tube lenses air; d 3; are the beam diameters. APPENDIX: DIAGRAM FOR THE CONTROL CIRCUIT Here, we resent the control circuit diagram (see Fig. 9) for driving the galvo system and a few notes. 73 Am. J. Phys., Vol. 85, No. 1, January 017 Aaratus and Demonstration Notes 73

7 Fig. 9. Comlete circuit diagram for driving the galvo system (OP1: Texas Instruments OPA548, OP: Analog Devices OP48GPZ, V: Intersil ISL1080CIH315Z-TK 1.5 V voltage reference, C: 0.1 lf ceramic, and C1: 1.6 nf ceramic). (1) The urose of the ISL1080CIH315Z-TK (Intersil) 1.5 V voltage reference and the 1 and 13-kX resistors is to achieve a level shifting from 0 to 3.3 V (Arduino outut) to 615 V. () The urose of the 0-X ower resistor is to dissiate most of the ower outut and also make the load more resistive rather than inductive. (3) The combination of the 13-kX resistor and the 0.1-lF caacitor in arallel forms a RC filter with time constant about 1.3 ms. This filter hels in stabilizing the outut, but is still fast enough so as not to slow down the resonse of the galvo. Consider the vectors of the ray of incidence ~i, the ray of reflection ~r, and the normal vector ^n to the mirror surface in one lane, as shown in Fig. 10(a). Since only the directions are relevant, we assume these vectors have unit length and lace them in a sherical coordinate system with the azimuth lane in age where h ¼ =. When the mirror is tilted horizontally (vertically), ^n is moved in the / (h) direction. The law of reflection allows us to write down the relationshi between them as and vector subtraction is to convert to Cartesian coordinates. Hence, ð ~iþ^n ¼ ði x n x þi y n y þi z n z Þ¼sinð= h s =Þ1= ffiffi ¼cosðh s =Þ1= ffiffi ; rx ¼½ð ~iþ^nšn x þi x ¼cosðh s =Þ1= ffiffi cosðh s =Þ1= ffiffiffi 1¼cos ðh s =Þ 1; r y ¼cos ðh s =Þ, and r z ¼ cosðh s =Þ1= ffiffiffi sin ð hs =Þ¼ sinh s = ffiffiffi. Converting back to sherical coordinates, r h ¼ cos 1 ðz=r r Þ, where r r ¼1. ~r þð ~i Þ¼½ð ~i Þ^nŠ^n: (A1) In the first and simler case, the mirror is tilted only in the azimuthal direction. All three vectors are therefore in the azimuth lane. If the mirror is tilted by a scan angle h s = in the / direction, the reflected ray ~r is deviated by h s, as illustrated in Fig. 10(b). This is the scan angle range for the horizontal direction. In the second case, the mirror is tilted by h s = in the h direction. The three vectors are set u in the sherical coordinates as, in the usual ðr; h; /Þ notation, ~i ¼ 1; ; ; ^n ¼ 1; h s ; ; and 4 ~r ¼ 1; h v; / v : (A) Here, h v is the quantity in ursuit, the angle of the reflected ray deviated from the azimuth lane. The vector ~r can now be calculated using Eq. (A1). One way to erform the scalar roduct Fig. 10. (a) The relationshi between ray of incidence ~i, normal vector of the mirror ^n, and the ray of reflection ~r. (b) The three vectors in the azimuthal lane when the mirror is tilted only in the / (horizontal) direction. 74 Am. J. Phys., Vol. 85, No. 1, January 017 Aaratus and Demonstration Notes 74

8 Therefore, r h ¼ cos 1 ðsinh s = ffiffiffi Þ.Forhs much smaller than 1, sinh s h s,sor h cos 1 ðh s = ffiffiffi Þ. Again for small hs, exanding r h at0gives,tofirstorder,r h = h s = ffiffi. Comaring with Eq. (A), we find the desired quantity h v ¼ h s = ffiffi. Finally, comaring the above two cases, for the same amount of tilting of the mirror, we found that the scan ffiffiffi range in the vertical direction is reduced by a factor of, due to the geometrical arrangement of the mirror. a) Electronic mail: jeh114@itt.edu b) Electronic mail: dursobr@itt.edu 1 F. Sitzer and B. Howarth, Princiles of Modern Instrumentation (Holt, Rinehart and Winston, 197). For examle, Zero galvanometer by Chauvin Arnoux. 3 R. P. Aylward, Advances and technologies of galvanometer-based otical scanners, Proc. SPIE 3787, 158 (1999). 4 M. D. Mccarty, U.S. atent,351,353 (13 June 1944). 5 J. S. Chandler, D. M. Orlicki, and J. M. Kresock, U.S. atent 5,80,377 (18 January 1994). 6 A. Gh. Podoleanu, G. M. Dobre, and D. A. Jackson, En-face coherence imaging using galvanometer scanner modulation, Ot. Lett. 3(3), (1998). 7 Tailored Light Laser Alication Technology, edited by R. Porawe (Sringer-Verlag, Heidelberg, 011). 8 D. Perrottet et al., Using Lasers to Dice Thin Silicon Wafers, Adv. Packag. 17, (008). 9 R. A. Ganeev, Laser Surface Interactions (Sringer Science & Business Media, Dordrecht, 014). 10 C. J. R. Sheard and D. M. Shotton, Confocal Laser Scanning Microscoy (Sringer-Verlag, Singaore, 1997). 11 S. Inoue, in Handbook of Biological Confocal Microscoy, 3rd ed., edited by J. B. Pawley (Sringer Science & Business Media, Dordrecht, 006), For examle, E. H. K. Stelzer, in Handbook of Biological Confocal Microscoy, 3rd ed., edited by J. B. Pawley (Sringer Science & Business Media, Dordrecht, 006), The manual for Galvo system GVS01 from Thorlabs, <htt:// 14 M. F. Ashby, H. Shercliff, and D. Cebon, Materials: Engineering, Science, Processing and Design, 3rd ed. (Butterworth-Heinemann, Oxford, 013), J. E. Shigley and C. R. Mischke, Mechanical Engineering Design, 5th ed. (McGraw-Hill, New York, 1989). 16 Since the mirror is laced 45 relative to the horizontal incident beam, for small scan angles the deflection of ffiffiffi the reflected beam in the vertical direction is reduced by a factor of, while the scan angle in the horizontal direction is not affected. ffiffi The result of this effect is that the field of view has an asect ratio of : See sulementary material at htt://dx.doi.org/ / for machine drawings and samle codes. 18 Technical datasheet for the Atmel rocessor SAM3X8E used in Arduino DUEs, <htt:// Microcontroller-SAM3X-SAM3A_Datasheet.df>. 19 Pythics Project, <htts://github.com/dursobr/ythics>. 0 The authors do not intend to make an imression that the resented design is comarable or suerior to the commercially-available units in its characterized erformance. This is a simle, inexensive, and robust alternative for those alications where our resented characteristics meet the criteria. 1 Imortant requirements for this alication are outut voltages (615 V) and the current limit. This alication draws a maximum of about 15 V/30 X 1 A. The noise from the ower suly has little effect on the erformance of the galvo. For an infinity-corrected microscoe objective, there must be a second lens for the collimated light from the focal oint of the objective to focus again to form an image. Only then is the magnification meaningful. Objective manufacturers secify 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 microscoy system around an objective, it can be modeled by a simle 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 examle, Olymus uses 180 mm while Mitutoyo uses 00 mm. See R. Juskaitis, in Handbook of Biological Confocal Microscoy, 3rd ed., edited by J. B. Pawley (Sringer Science & Business Media, Dordrecht, 006), K. Iakoubovskii, G. J. Adriaenssens, and M. Nesladek, Photochromism of vacancy-related centres in diamond, J. Phys.: Condens. Matter 1, (000). 4 T. Dabbs and M. Glass, Single-mode fibres used as confocal microscoe inholes, Al. Ot. 31(6), (199). 5 P. Delaney and M. Harris, in Handbook of Biological Confocal Microscoy, 3rd ed., edited by J. B. Pawley (Sringer Science & Business Media, Dordrecht, 006), J. Hecht, Understanding Fiber Otics, 3rd ed. (Prentice Hall, Uer Saddle River, NJ, 1999). 75 Am. J. Phys., Vol. 85, No. 1, January 017 Aaratus and Demonstration Notes 75