**4.1 Theoretical module**

CGHs treated in this module are Fourier holograms, main application is optical interconnects (fan-out). The reproduction setup is shown in Fig. 5 (a).

At its simplest, a CGH is basically a diffraction grating composed by a 2D unit cell, repeated along the hologram surface. Let's consider the diffraction grating shown in Fig. 5 (b).

When this grating is illuminated by a collimated monochromatic beam, a Fraunhofer diffraction pattern is obtained in the focal plane of the lens L (*i.e.* Fourier transform of the complex amplitude transmittance of the diffraction grating). Spacing between diffraction peaks is given by (Hecht, 1988):

$$\mathbf{x} = \frac{\lambda f}{d} \tag{1}$$

4 Will-be-set-by-IN-TECH

(a) Laboratory setup

(b) Picture of the actual laboratory assembly

CGHs have long been used in optical processing information, optical interconnects, interferometry and health diagnosis, to name just a few relevant applications (Yaroslavsky & Astola, 2009). Advances in computer power, together with the development of sophisticated manufacturing methods, are causing CGHs to become increasingly efficient and complex.

CGHs treated in this module are Fourier holograms, main application is optical interconnects

At its simplest, a CGH is basically a diffraction grating composed by a 2D unit cell, repeated

When this grating is illuminated by a collimated monochromatic beam, a Fraunhofer diffraction pattern is obtained in the focal plane of the lens L (*i.e.* Fourier transform of the complex amplitude transmittance of the diffraction grating). Spacing between diffraction

*<sup>x</sup>* <sup>=</sup> *<sup>λ</sup> <sup>f</sup>*

*<sup>d</sup>* (1)

along the hologram surface. Let's consider the diffraction grating shown in Fig. 5 (b).

Fig. 3. Laboratory experiments on diffraction

(fan-out). The reproduction setup is shown in Fig. 5 (a).

**4.1 Theoretical module**

peaks is given by (Hecht, 1988):


Fig. 4. Main interface for laboratory experiments

where *d* is the grating spacing, *f* is the focal length of the Fourier lens, and *λ* is wavelength of the collimated light beam. Relative intensities of the diffraction orders are proportional to the grating structure *a*/*d*. In any CGH, it is important to maximize light on the desired diffraction order (usually +1). Diffraction efficiency DE, defined as:

$$\text{DE} = \frac{\text{Light in the desired diffracted order}}{\text{Total incident light}} \tag{2}$$

measures such light maximization. To this end, when the basic CGH cell is calculated, such 2D cell is repeated to form the CGH structure; spatial invariance of the Fourier transform means that every single cell produces the same diffraction pattern at the output plane, contributing to increased DE. The type of optical material in which the CGH is implemented also contributes to have a good DE.

CGHs calculated in section 4.2 are binary-only (*i.e.* pixels have only two possible values, black or white). Depending on the type of physical object where the CGH is implemented, it can be a Binary Amplitude Hologram (*i.e.* photographic film, where black pixels correspond to dark zones and white pixels are transparent zones in the film) or a Phase-only Hologram (for instance, using a Liquid Crystal Spatial Light Modulator, where the two possible orientation of the liquid crystal molecules correspond to phase states differing by *π*).

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A Contribution to Virtual Experimentation in Optics 363

Once the CGH has been calculated, the performance of such CGH can be also checked from this window. To this end, a valid CGH image (either freshly calculated or pre-loaded from the PC) must be displayed on the right-side image frame in Fig. 7(a). By pressing on "DEPECA" icon (or, alternatively, selecting Tools, Image calculation on the Menu, shortcut *Ctrl + I*), the inverse Fourier transform is performed, and the object image is then reconstructed. Fig. 8 shows two CGH masks built from the same unit cell, calculated using the simulated annealing algorithm in Fig. 7. Each mask has 2 × 2 and 4 × 4 times the unit cell, respectively. Target output for such unit cell is a 4 × 4 fan-out array of light spots at the Fourier plane in

When the target output is symmetrical (as in Fig. 8), due to the symmetry properties of the Fourier Transform binary CGHs, only half of the output target is needed to be defined (specular image appears automatically at the output plane) (Morrison, 1992). This reduces

Fig. 8 (a.2) and (b.2) show simulations of the optical power spectrum detected by physical sensors. This power spectrum is proportional to the square of the 2-D complex Fourier transform amplitude of the CGH (Hecht, 1988). Low spatial frequencies are near the center of the spectrum (zero spatial frequency), and high frequencies are farther away from the centre, as usual in optical power spectrum representations (Poon & Banerjee, 2001). Simulations show that spot spacing is inversely proportional to the corresponding size cell, as shown in Equation

Fig. 6. Main interface for laboratory experiments

significantly the computing time for the CGH (Samus, 1995).

1, where *d* is the size of the unit cell.

Fig. 5.

Fig. 5. (a) Reproduction setup of a Fourier CGH (b) Simple diffraction grating

The software developed includes a theoretical module to explain the basis of the CGHs to the user. Fig 6 shows one of the multi-page theoretical screens. Applications, numerical computing algorithms, and setup schemes for physical reproduction of CGHs are fully explained in this module.

### **4.2 Simulation module**

Fig. 7(a) shows the main window for CGH calculation. The left-side image frame displays the object image, while the right-side frame stores the calculated CGH. A blue background indicates which is the active frame, either CGH or object image.

Holograms are calculated from pre-stored object images loaded on the left-side image frame on Fig. 7(a)). The following algorithms can be selected, with their corresponding parameters, as shown in Fig. 7(b):


The resolution of the image clearly influences the hologram computing time. The CGH calculated is represented on the right-side image frame on Fig. 7(a), and can be stored on the computer using different format files (e.g. .BMP, .JPG, . . . ).

6 Will-be-set-by-IN-TECH

CGH

Output plane

Coherent light beam

(a)

Fourier

lens CGH

Fig. 5. (a) Reproduction setup of a Fourier CGH (b) Simple diffraction grating

*f*

(b)

The software developed includes a theoretical module to explain the basis of the CGHs to the user. Fig 6 shows one of the multi-page theoretical screens. Applications, numerical computing algorithms, and setup schemes for physical reproduction of CGHs are fully

Fig. 7(a) shows the main window for CGH calculation. The left-side image frame displays the object image, while the right-side frame stores the calculated CGH. A blue background

Holograms are calculated from pre-stored object images loaded on the left-side image frame on Fig. 7(a)). The following algorithms can be selected, with their corresponding parameters,

The resolution of the image clearly influences the hologram computing time. The CGH calculated is represented on the right-side image frame on Fig. 7(a), and can be stored on

Collimated beam

Laser

explained in this module.

**4.2 Simulation module**

as shown in Fig. 7(b):

• Detour phase (Levy et al., 1998)

• Simulated annealing (Kirkpatrick, 1983)

Spatial filter

*d a*

indicates which is the active frame, either CGH or object image.

the computer using different format files (e.g. .BMP, .JPG, . . . ).

• Fourier transform (Wyrowsky & Bryngdahl, 1988)

Fourier lens

*f*

Output plane

Fig. 6. Main interface for laboratory experiments

Once the CGH has been calculated, the performance of such CGH can be also checked from this window. To this end, a valid CGH image (either freshly calculated or pre-loaded from the PC) must be displayed on the right-side image frame in Fig. 7(a). By pressing on "DEPECA" icon (or, alternatively, selecting Tools, Image calculation on the Menu, shortcut *Ctrl + I*), the inverse Fourier transform is performed, and the object image is then reconstructed.

Fig. 8 shows two CGH masks built from the same unit cell, calculated using the simulated annealing algorithm in Fig. 7. Each mask has 2 × 2 and 4 × 4 times the unit cell, respectively. Target output for such unit cell is a 4 × 4 fan-out array of light spots at the Fourier plane in Fig. 5.

When the target output is symmetrical (as in Fig. 8), due to the symmetry properties of the Fourier Transform binary CGHs, only half of the output target is needed to be defined (specular image appears automatically at the output plane) (Morrison, 1992). This reduces significantly the computing time for the CGH (Samus, 1995).

Fig. 8 (a.2) and (b.2) show simulations of the optical power spectrum detected by physical sensors. This power spectrum is proportional to the square of the 2-D complex Fourier transform amplitude of the CGH (Hecht, 1988). Low spatial frequencies are near the center of the spectrum (zero spatial frequency), and high frequencies are farther away from the centre, as usual in optical power spectrum representations (Poon & Banerjee, 2001). Simulations show that spot spacing is inversely proportional to the corresponding size cell, as shown in Equation 1, where *d* is the size of the unit cell.

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A Contribution to Virtual Experimentation in Optics 365

(a.1) 2 × 2 (b.1) 4 × 4

(a.2) (b.2)

(a.3) (b.3)

Fig. 8. CGH cells replicated (a.1) 2 × 2 and (b.1) 4 × 4 times; (a.2) and (b.2) simulated optical

Acousto-optics describes the interaction of sound with light (Saleh & Teich, 1991). A sound wave unleashed on an optical medium creates a disturbance in the refractive index of the medium. The sound can then control a light beam hitting the medium. This fact, known as acousto-optical (AO) effect is used in various devices, such as beam deflectors, optical

modulators, filters, isolators and spectrum analyzers, among others.

output (a.3) and (b.3) 3-D intensity profiles

**5. Acousto-optical effect**

(a) Main window for CGH calculation


Fig. 7. CGH simulation module

### **4.3 Laboratory experimentation module**

Fig. 9 displays the actual implementation of the optical setup from Fig. 5.

A webcam is placed at the output (Fourier) plane to collect the diffraction pattern produced by a CGH illuminated with a coherent, collimated optical beam from a He-Ne laser.

To show the performance of the simulation module, some fan-out CGHs have been implemented on a photographic film, as shown in Fig. 10. The presence of non-developed grains in the emulsion increases the undesired central DC spot in the diffraction pattern, as shown in Fig. 11.

Image acquisition and processing is managed from the interface shown in Fig. 12. The user can also make a comparison between theoretical CGH output, simulated output using the computing tool in Section 4.2, and real CGH output captured by the webcam placed at the Fourier plane in Fig. 9. Comparison is made in two ways: similarity (i.e. digital substraction of images), and correlation between images.

8 Will-be-set-by-IN-TECH

(a) Main window for CGH calculation

(b) Parameter setup for computing

A webcam is placed at the output (Fourier) plane to collect the diffraction pattern produced

To show the performance of the simulation module, some fan-out CGHs have been implemented on a photographic film, as shown in Fig. 10. The presence of non-developed grains in the emulsion increases the undesired central DC spot in the diffraction pattern, as

Image acquisition and processing is managed from the interface shown in Fig. 12. The user can also make a comparison between theoretical CGH output, simulated output using the computing tool in Section 4.2, and real CGH output captured by the webcam placed at the Fourier plane in Fig. 9. Comparison is made in two ways: similarity (i.e. digital substraction

by a CGH illuminated with a coherent, collimated optical beam from a He-Ne laser.

algorithms

Fig. 9 displays the actual implementation of the optical setup from Fig. 5.

Fig. 7. CGH simulation module

shown in Fig. 11.

**4.3 Laboratory experimentation module**

of images), and correlation between images.

Fig. 8. CGH cells replicated (a.1) 2 × 2 and (b.1) 4 × 4 times; (a.2) and (b.2) simulated optical output (a.3) and (b.3) 3-D intensity profiles

### **5. Acousto-optical effect**

Acousto-optics describes the interaction of sound with light (Saleh & Teich, 1991). A sound wave unleashed on an optical medium creates a disturbance in the refractive index of the medium. The sound can then control a light beam hitting the medium. This fact, known as acousto-optical (AO) effect is used in various devices, such as beam deflectors, optical modulators, filters, isolators and spectrum analyzers, among others.

in Optics 11

A Contribution to Virtual Experimentation in Optics 367

Fig. 11. (Left) Output at Fourier plane of 4 × 4 dots fan-out CGHs consisting of AA = 4 × 4

(characterized by the refractive index, *n*, and the acoustic velocity in the material, *VS*), and the RF waveform (characterized by its amplitude *A* and frequency *fS*). By these conditions,

of input parameters is calculated. The simulation module can also create a video sequence, which shows graphically the phenomenon of acousto-optical interaction from a 2D or 3D perspective, as shown in Figure 14 (b). The video is also saved as AVI file for later viewing.

Figure 15 shows the block diagram of the experimental setup. A radio frequency (RF) electronics module generates a 24 MHz wave which impinges the acousto-optical device (AOD), thus producing a diffraction grating along the material. The acousto-optical interaction is observed when a laser beam coming out of a laser pointer crosses the AOD

2*n*Λ*<sup>S</sup>*

<sup>≈</sup> *<sup>λ</sup><sup>O</sup> fS nVS*

✁ CALCULATE DEVIATION button, the deflection angle as a function

(3)

*<sup>θ</sup><sup>D</sup>* <sup>=</sup> <sup>2</sup>*θ<sup>B</sup>* <sup>=</sup> 2 sin−<sup>1</sup> *<sup>λ</sup><sup>O</sup>*

AA

BB

✄ ✂

**5.3 Laboratory experimentation module**

When pressing the

and BB = 2 × 2 unit cell. (Right) Corresponding 3D intensity profiles

the first-order deflection angle under the Bragg regime is given by:

Fig. 9. CGH experimental setup

(a) CGH on photographic film

Fig. 10. (a) CGH implemented on photographic film; (c), (d) Microscopic details showing development imperfections

### **5.1 Theoretical module**

This module explains the basis of AO phenomena: Raman-Nath and Bragg configurations, AO materials, figures of merit, etc. The user can navigate interactively through different tutorials, as shown in Fig. 13. Documentation and a user's manual are also available, including datasheets of the components used in section 5.3.

### **5.2 Simulation module**

Acousto-optical virtual experiments are performed within this module. Fig. 14 shows the main interface of the simulation module. The user can choose one of the two interaction regimes (Bragg or Raman-Nath), explained in the previous theoretical module. The application allows to select the light source wavelength (*λO*), the acousto-optical material 10 Will-be-set-by-IN-TECH

(b) ×10 (c) ×40

Fig. 10. (a) CGH implemented on photographic film; (c), (d) Microscopic details showing

including datasheets of the components used in section 5.3.

This module explains the basis of AO phenomena: Raman-Nath and Bragg configurations, AO materials, figures of merit, etc. The user can navigate interactively through different tutorials, as shown in Fig. 13. Documentation and a user's manual are also available,

Acousto-optical virtual experiments are performed within this module. Fig. 14 shows the main interface of the simulation module. The user can choose one of the two interaction regimes (Bragg or Raman-Nath), explained in the previous theoretical module. The application allows to select the light source wavelength (*λO*), the acousto-optical material

Fig. 9. CGH experimental setup

(a) CGH on photographic film

development imperfections

**5.1 Theoretical module**

**5.2 Simulation module**

Fig. 11. (Left) Output at Fourier plane of 4 × 4 dots fan-out CGHs consisting of AA = 4 × 4 and BB = 2 × 2 unit cell. (Right) Corresponding 3D intensity profiles

(characterized by the refractive index, *n*, and the acoustic velocity in the material, *VS*), and the RF waveform (characterized by its amplitude *A* and frequency *fS*). By these conditions, the first-order deflection angle under the Bragg regime is given by:

$$
\theta\_D = 2\theta\_B = 2\sin^{-1}\frac{\lambda\_O}{2n\Lambda\_S} \approx \frac{\lambda\_O f\_S}{nV\_S} \tag{3}
$$

When pressing the ✄ ✂ ✁ CALCULATE DEVIATION button, the deflection angle as a function of input parameters is calculated. The simulation module can also create a video sequence, which shows graphically the phenomenon of acousto-optical interaction from a 2D or 3D perspective, as shown in Figure 14 (b). The video is also saved as AVI file for later viewing.

### **5.3 Laboratory experimentation module**

Figure 15 shows the block diagram of the experimental setup. A radio frequency (RF) electronics module generates a 24 MHz wave which impinges the acousto-optical device (AOD), thus producing a diffraction grating along the material. The acousto-optical interaction is observed when a laser beam coming out of a laser pointer crosses the AOD

in Optics 13

A Contribution to Virtual Experimentation in Optics 369

Diffraction orders m = +1

ω0 + Ω <sup>S</sup>

z

m=0

ω0

B

θ θ

x

 Acoustic wavefront

θ<sup>B</sup> <sup>B</sup>

Ω <sup>S</sup> (a) AO interaction under Bragg regime

(b) Main window of the AO theory module

 Input light beam

s(t)

*L*

ω0

Fig. 13. AO theoretical module


Fig. 12. CGH laboratory module: main window


Table 1. Main specifications of the AOD employed

while the RF wave is on; under such circumstances, the light beam is deviated, according to Equation 3.

Laser ignition and RF waveform generation are controlled by the software module through the RS232 port. Finally, the diffracted beam is projected on a screen for direct viewing and/or detection by a suitable sensor (*i.e.* photodetector, optical power meter, etc.).

The acousto-optical device (AOD) shown in Fig 16 has been employed. This AOD was acting as Q-switch on a dismantled Nd:YAG laser. Table 1 shows main parameters of this AOD.

For this application, a red laser pointer with wavelength *λ* = 670 nm has been used. According to Equation 3, the theoretical deflection angle for this red light source is:

12 Will-be-set-by-IN-TECH

Fig. 12. CGH laboratory module: main window

Table 1. Main specifications of the AOD employed

Equation 3.

**Parameter Value**

RF Frequency 24 MHz Clear Aperture 8 × 10 mm

Input impedance 5 Ω

detection by a suitable sensor (*i.e.* photodetector, optical power meter, etc.).

According to Equation 3, the theoretical deflection angle for this red light source is:

Interaction Material Fused Silica Wavelength 1047 U 1064nm ˝

Acoustic Mode Compressional or Shear

while the RF wave is on; under such circumstances, the light beam is deviated, according to

Laser ignition and RF waveform generation are controlled by the software module through the RS232 port. Finally, the diffracted beam is projected on a screen for direct viewing and/or

The acousto-optical device (AOD) shown in Fig 16 has been employed. This AOD was acting as Q-switch on a dismantled Nd:YAG laser. Table 1 shows main parameters of this AOD. For this application, a red laser pointer with wavelength *λ* = 670 nm has been used.

(a) AO interaction under Bragg regime

(b) Main window of the AO theory module

Fig. 13. AO theoretical module

in Optics 15

A Contribution to Virtual Experimentation in Optics 371

A separation Δ*x* = 1 cm between the diffracted and non-diffracted beams is achieved at a

The incoming light beam crossing the AOD is deviated as long as a proper RF signal is injected through the AOD transducer. To this end, a 24 MHz signal is generated using a IQXO-350-C,

This RF power output is too low to properly observe the acousto-optical phenomenon. A

Therefore, a BGD502 amplifier with *GdB* = 18.25 dB is employed to amplify the RF output

RF signal generation and laser diode injection are managed via the RS232 port on the control PC. Tx and Rx signals RS232 send bit patterns with voltage levels of +15 V or -15 V. Since the RF generator circuit needs TTL levels (0 V - 5 V), a RS232-TTL level adaptation is implemented through a MAX232 integrated circuit. The flip-flop CD4027BM transforms the last bit of the TTL data frame provided by the MAX232 to a fixed voltage level (0V or 5V) which enables

<sup>=</sup> 10 log <sup>1000</sup>

*P* = *V* · *I* = 1, 8 V · 26, 2 mA = 47, 16 mW (6)

(b) Setup for AO experiments

47, 16 <sup>=</sup> 13, 26 *dB* (7)

(a) Main window of the AO laboratory module

distance *L* = 10 m away from the AOD output.

which gives an RF output power of:

signal.

Fig. 15. Acousto-optical laboratory experimentation module

good figure for this RF power output is 1 W, which gives a gain *GdB* of:

*Pin*

*GdB* <sup>=</sup> 10 log *Pout*

(a) Main window of the AO simulation module

(b) 3D video animation illustrating AO interaction

Fig. 14. AO simulation module

$$
\theta\_D = 0.00091943 \text{ rad} \tag{4}
$$

Since this angle is small enough, the following assumption can be made:

$$
\sin \theta\_D \approx \theta\_D = \frac{\Delta x}{L} \tag{5}
$$

14 Will-be-set-by-IN-TECH

(a) Main window of the AO simulation module

(b) 3D video animation illustrating AO interaction

sin *<sup>θ</sup><sup>D</sup>* <sup>≈</sup> *<sup>θ</sup><sup>D</sup>* <sup>=</sup> <sup>Δ</sup>*<sup>x</sup>*

Since this angle is small enough, the following assumption can be made:

*θ<sup>D</sup>* = 0.00091943 rad (4)

*<sup>L</sup>* (5)

Fig. 14. AO simulation module

A separation Δ*x* = 1 cm between the diffracted and non-diffracted beams is achieved at a distance *L* = 10 m away from the AOD output.

The incoming light beam crossing the AOD is deviated as long as a proper RF signal is injected through the AOD transducer. To this end, a 24 MHz signal is generated using a IQXO-350-C, which gives an RF output power of:

$$P = V \cdot I = 1,8\,\text{V} \cdot 26,2\,\text{mA} = 47,16\,\text{mW} \tag{6}$$

This RF power output is too low to properly observe the acousto-optical phenomenon. A good figure for this RF power output is 1 W, which gives a gain *GdB* of:

$$G\_{dB} = 10 \log \frac{P\_{out}}{P\_{in}} = 10 \log \frac{1000}{47.16} = 13.26 \, dB \tag{7}$$

Therefore, a BGD502 amplifier with *GdB* = 18.25 dB is employed to amplify the RF output signal.

RF signal generation and laser diode injection are managed via the RS232 port on the control PC. Tx and Rx signals RS232 send bit patterns with voltage levels of +15 V or -15 V. Since the RF generator circuit needs TTL levels (0 V - 5 V), a RS232-TTL level adaptation is implemented through a MAX232 integrated circuit. The flip-flop CD4027BM transforms the last bit of the TTL data frame provided by the MAX232 to a fixed voltage level (0V or 5V) which enables

in Optics 17

A Contribution to Virtual Experimentation in Optics 373

**Regime** *Ii* (*μ* W) *Ii* (*n* W) **DE (%)** Raman-Nath 4.55 68 1,5 Bragg 4.55 98 2,2

the Bragg angle, the Bragg regime shown in Fig. 17 (b) is obtained, and the single diffracted

The work presented in this chapter aims to explain some optical phenomena from an educational perspective. The tools implemented combine virtual and real experimentation, and they can be used as laboratory material for technical studies in science and engineering. All the modules described in this chapter share in common the diffracting behavior of light. Nevertheless, there are other modules available (*i.e.* Moiré effect, Radiometry and

To date, these software tools need to be installed on the PC. Nevertheless, there is an on-going project to run them directly from a web browser. Other further improvements include:

• Interaction with a Spatial Light Modulator to dynamically display the calculated CGHs.

• Integration of a photodetector within the Laboratory module for measuring and plotting

• Optical design to reduce the total optical path and improve the detection at the output

• Characterization of the AOD (bandwidth, rise-time, etc.) by modulating the 24MHz RF

Brown, B. R. & Lohmann, A. W. (1966). Complex spatial filtering with binary masks, *Applied*

Carnicer, A. (2010). *The JOptics Course*, www.ub.es/javaoptics, University of Barcelona. Carreño, F. (2010). *Group of Teaching Optics*, www.ucm.es/info/opticaf, University

Kirkpatrick, S. (1983). Optimisation by simulated annealing filtering with binary masks,

Levy, U; Marom, E. & Mendlovic, D. (1998). Modifications of detour phase computer-generated holograms, *Applied Optics*, Vol. 37, Issue 14, 3044 – 3052. *MATLAB - The Language Of Technical Computing*, www.mathworks.com/products/matlab. Morrison, R. L. (1992). Symmetries that simplify the design of spot array phase gratings,

*Journal of the Optical Society of America - A*, Vol. 9, Issue 3, 464 – 471.

Photometry) or under development (*i.e.* Theory of color, Geometrical Optics).

Table 2. DE measured on Fig. 17 experiments

**6. Conclusions and further work**

**Computer Generated Holograms tool:**

the diffracted light beams.

**Acousto-optics tool:**

plane.

waveform.

**7. References**

• Implementation of new computing algorithms.

*Optics*, Vol. 5, Issue 6, 967 – 969.

Complutense of Madrid. Hecht, E. (1998). Optics, Addison-Wesley.

*Science*, Vol. 220, 671 – 680.

beam reaches its greatest intensity, as shown in Table 2.

Fig. 16. AOD used for experimental verification

(5V = logic 1) or disables (0V = logical 0) the generation of RF waveform and turning on / off the laser diode transmitter.

Fig. 17 shows the output light beam after passing through the AOD when the RF signal is activated. As predicted by theory, the diffraction efficiency of the diffracted beam depends on the geometry of interaction between the beam and the AO material. In the case of normal incidence (Raman-Nath regime, Fig. 17 (a)), two diffraction orders occur, one on each side of the central DC spot corresponding to the non-diffracted light beam. Rotating the AOD to get

(a) Raman-Nath regime (b) Bragg regime

Fig. 17. Output beam diffracted by the AOD under different interaction regimes

16 Will-be-set-by-IN-TECH

(5V = logic 1) or disables (0V = logical 0) the generation of RF waveform and turning on / off

Fig. 17 shows the output light beam after passing through the AOD when the RF signal is activated. As predicted by theory, the diffraction efficiency of the diffracted beam depends on the geometry of interaction between the beam and the AO material. In the case of normal incidence (Raman-Nath regime, Fig. 17 (a)), two diffraction orders occur, one on each side of the central DC spot corresponding to the non-diffracted light beam. Rotating the AOD to get

(a) Raman-Nath regime (b) Bragg regime

Fig. 17. Output beam diffracted by the AOD under different interaction regimes

Fig. 16. AOD used for experimental verification

the laser diode transmitter.


Table 2. DE measured on Fig. 17 experiments

the Bragg angle, the Bragg regime shown in Fig. 17 (b) is obtained, and the single diffracted beam reaches its greatest intensity, as shown in Table 2.

### **6. Conclusions and further work**

The work presented in this chapter aims to explain some optical phenomena from an educational perspective. The tools implemented combine virtual and real experimentation, and they can be used as laboratory material for technical studies in science and engineering. All the modules described in this chapter share in common the diffracting behavior of

light. Nevertheless, there are other modules available (*i.e.* Moiré effect, Radiometry and Photometry) or under development (*i.e.* Theory of color, Geometrical Optics).

To date, these software tools need to be installed on the PC. Nevertheless, there is an on-going project to run them directly from a web browser. Other further improvements include:

### **Computer Generated Holograms tool:**


### **Acousto-optics tool:**


### **7. References**

Brown, B. R. & Lohmann, A. W. (1966). Complex spatial filtering with binary masks, *Applied Optics*, Vol. 5, Issue 6, 967 – 969.

Carnicer, A. (2010). *The JOptics Course*, www.ub.es/javaoptics, University of Barcelona.

Carreño, F. (2010). *Group of Teaching Optics*, www.ucm.es/info/opticaf, University Complutense of Madrid.

Hecht, E. (1998). Optics, Addison-Wesley.


*MATLAB - The Language Of Technical Computing*, www.mathworks.com/products/matlab.

Morrison, R. L. (1992). Symmetries that simplify the design of spot array phase gratings, *Journal of the Optical Society of America - A*, Vol. 9, Issue 3, 464 – 471.

Poon, T.C. & Banerjee, P.P (2001). *Contemporary Optical Image Processing with Matlab*, Elsevier Science.

Saleh, B. E. A. & Teich, M. (1991). *Fundamental of Photonics*, John Wiley & Sons.


Yaroslavsky, L. & Astola, J. (2009). *Introduction to Digital Holography*, Bentham Science.

18 Will-be-set-by-IN-TECH

374 Advanced Holography – Metrology and Imaging

Poon, T.C. & Banerjee, P.P (2001). *Contemporary Optical Image Processing with Matlab*, Elsevier

Samus, S. (1995). *Computer Design and Optimisation of Holographic Phase Elements*, Ph.D. Thesis,

Wyrowsky, F. & Bryngdahl, O. (1988). Iterative Fourier-transform algorithm applied to

Saleh, B. E. A. & Teich, M. (1991). *Fundamental of Photonics*, John Wiley & Sons.

computer holography, *J. Opt. Soc. Am. A*, Vol. 5, 1058 – 1065.

Yaroslavsky, L. & Astola, J. (2009). *Introduction to Digital Holography*, Bentham Science.

Science.

The University of Edinburgh.
