## Method for characterization of diffusion properties of photopolymerisable systems

Optics Express, Vol. 16, Issue 12, pp. 8487-8497 (2008)

http://dx.doi.org/10.1364/OE.16.008487

Acrobat PDF (212 KB)

### Abstract

A novel approach for measuring the diffusion coefficients in photopolymerisable materials is proposed. The method is based on studying the evolution of the surface relief profile in a single illuminated spot using an interferometric surface profiler. It is shown that the observed post-exposure swelling in the illuminated spot is due to mass-transport of monomer from the unexposed to the exposed area driven by a monomer concentration gradient set up by the monomer polymerization in the exposed area. Appropriate choice of the thickness of the studied layers ensures both lateral movement of monomer and negligible contribution from the depth. The diffusion coefficient is retrieved from the standard one-dimensional diffusion equation where the height of the profile in the center of the illuminated spot is used instead of the monomer concentration. In contrast to other techniques for measuring the diffusion in photopolymerisable materials, no assumptions or preliminary information about the polymerization rates are required. It is shown how the method can be used for studying the intensity and polymer density dependence of diffusion coefficient.

© 2008 Optical Society of America

## 1. Introduction

1. T. J. Trout, J. J. Schmieg, W. Y. Gambogi, and A. M. Weber, “Optical photopolymers: Design and applications,” Adv. Mat. **10**, 1219–1224 (1998). [CrossRef]

2. A. Sullivan, M. Grabowski, and R. McLeod, “Three-dimensional direct-write lithography into photopolymer,” Appl. Opt. **46**, 295–301 (2007). [CrossRef] [PubMed]

3. S. Guntaka, V. Toal, and S. Martin, “Holographically recorded photopolymer diffractive optical element for holographic and electronic speckle-pattern Interferometry,” Appl. Opt. **41**, 7475–7479 (2002). [CrossRef] [PubMed]

4. H. J. Zhou, V. Morozov, and J. Neff, “Characterization of DuPont photopolymers in infrared light for free-space optical interconnects,” Appl. Opt. **34**, 7457–7459 (1995). [CrossRef] [PubMed]

5. H. Sherif, I Naydenova, S. Martin, C. McGinn, and V. Toal, “Characterization of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing,” J. Opt. A:Pure&Appl. Opt. **7**, 255–261 (2005). [CrossRef]

8. G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. **41**, 1929–1939 (1994). [CrossRef]

9. V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. **81**, 5913–5923 (1997). [CrossRef]

9. V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. **81**, 5913–5923 (1997). [CrossRef]

12. I. Naydenova, R. Jallapuram, R. Howard, S. Martin, and V. Toal, “Investigation of the Diffusion Processes in a Self-Processing Acrylamide-Based Photopolymer System,” Appl. Opt. **43**, 2900–2905 (2004). [CrossRef] [PubMed]

## 2. Experimental details

14. S. Martin, C. A. Feely, and V. Toal, “Holographic recording characteristics of an acrylamide-based photopolymer,” Appl. Opt. **36**, 5757–5768 (1997). [CrossRef] [PubMed]

*t*°=21–23°C and 40–60% relative humidity) was about 35 µm.

^{2}for example) the sample absorption is approximately 4 to 50 times smaller than the initial absorption. Having in mind that 1/12 of the initial exposure is delivered at each measurement the amount of absorbed energy during the measurement is between 1/48 and 1/600 of the absorption during the initial exposure. Therefore, we can assume that the process of obtaining the profile did not change the sample substantially and did not cause further polymerization.

## 3. Results and discussion

*R*, from the aperture to the screen where the diffraction light is observed to be larger compared to aperture size, and the radius of aperture,

*a*, not to be much larger than the wavelength of light,

*λ*, i.e

*R*>

*a*/

^{2}*λ*. Simple calculations showed that in our case (

*a*=0.5mm,

*λ*=554nm and

*R*=220mm)

*a*

^{2}/

*λ*is 451 that is more than two times larger than

*R*(220mm), so the condition of observation of Airy pattern is not fulfilled. Therefore we can concluded that the Airy pattern resulted from diffraction from diaphragm 1mm in diameter can not be observed at plane positioned 220 mm apart from the diaphragm. Only for further clarification we would like to note that in our set-up the Airy pattern would be visible at the observation plane if the size of the used diaphragm is smaller than 0.3mm or the observation plane is more than 451mm apart from the diaphragm.

^{2}for a time of 30s. The post-exposure time dependence of the profile height at the centre of the spot is presented in Fig. 2(b) where

*t*=0 is defined as the time at the end of the exposure.

*n*and Δ

*h*, respectively) the first issue that should be addressed concerns the origin of the observed profile changes. In the case of normal light incidence the overall phase change Δ

*φ*initiated by refractive index and surface shape variation (Δ

*n*and Δ

*h*) can be estimated from the expression:

*λ*is the wavelength of light and Δ

*φ*and Δ

_{n}*φ*are the phase change contributions of refractive index

_{h}*n*and surface height

*h*, respectively. Therefore the ratio of the influences of

*n*and

*h*on Δ

*φ*can be estimated from:

*n*of the polymer layer is about 1.5, for Δ

*n*/

*n*we obtain a value of about 7×10

^{-5}assuming that in the case of short exposure the refractive index change is approximately 10

^{-4}[12

12. I. Naydenova, R. Jallapuram, R. Howard, S. Martin, and V. Toal, “Investigation of the Diffusion Processes in a Self-Processing Acrylamide-Based Photopolymer System,” Appl. Opt. **43**, 2900–2905 (2004). [CrossRef] [PubMed]

*t*=0–15s Δ

*h*=77nm and

*h*=37nm, so Δ

*h*/

*h*=1.9 and decreases to about 8.10

^{-3}for

*t*=90–120s (Δ

*h*=1nm,

*h*=127nm). The ratio between Δ

*φ*and Δ

_{h}*φ*calculated from Eq. (2) changes from about 2.7×10

_{n}^{4}to 110. Consequently, in the worst case, the phase change contribution of the height of the surface profile is about 110 times greater than the refractive index contribution. This leads to the conclusion that the observed profile changes are mainly due to shape changes.

### 3.1 Surface relief profile evolution

9. V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. **81**, 5913–5923 (1997). [CrossRef]

12. I. Naydenova, R. Jallapuram, R. Howard, S. Martin, and V. Toal, “Investigation of the Diffusion Processes in a Self-Processing Acrylamide-Based Photopolymer System,” Appl. Opt. **43**, 2900–2905 (2004). [CrossRef] [PubMed]

**43**, 2900–2905 (2004). [CrossRef] [PubMed]

16. C. Croutxe-Barghorn and D. J. Lougnot, “Use of self-processing dry photo-polymers for the generation of relief optical elements: a photochemical study,” Pure Appl. Opt. **5**, 811–827 (1996). [CrossRef]

17. J. Neumann, K. S. Wieking, and D. Kip, “Direct laser writing of surface reliefs in dry, self-developing photopolymer films,” Appl. Opt. **38**, 5418–5421 (1999). [CrossRef]

18. I. Naydenova, E. Mihaylova, S. Martin, and V. Toal, “Holographic patterning of acrylamide-based photopolymer surface,” Opt. Express **13**, 4878–4889 (2005). [CrossRef] [PubMed]

19. K. Pavani, I. Naydenova, S. Martin, and V. Toal, “Photoinduced surface relief studies in an acrylamide-based photopolymer,” J. Opt. A: Pure Appl. Opt. **9**, 43–48 (2007). [CrossRef]

14. S. Martin, C. A. Feely, and V. Toal, “Holographic recording characteristics of an acrylamide-based photopolymer,” Appl. Opt. **36**, 5757–5768 (1997). [CrossRef] [PubMed]

^{2}intensity for 30 s leads to increase of temperature in the layer by ten degrees resulting in thermal expansion of 40 nm. Because the transmittance of the layers at 554nm is about 60%, in the calculations we assumed that 40% of the incident energy is absorbed and transformed into heat. The values of specific heat capacity of 1650 Jkg

^{-1}K

^{-1}, density of 1200 kgm

^{-3}and linear thermal expansion of 10

^{-4}K

^{-1}[20] are used in the calculations. The higher values of calculated thermal expansion as compared to the measured showed that the amount of energy that is transformed into heat is less than we have assumed. This can be explained with the decrease of the sensitizing dye absorption with time that will lead to decrease in absorbed energy with time. Further, considering both that for monomer-containing samples the surface changes about by 120nm (Fig.2) and that the surface does not change for monomer-free samples we can conclude that the movement of monomer is responsible for the swelling in the illuminated area.

*r*is the radius of the spot and

*D*and τ are diffusion coefficient and diffusion time, τ should be expected to increase linearly with square of the spot radius [10

10. V. Moreau, Y. Renotte, and Y. Lion, “Characterization of DuPont photopolymer: determination of kinetic parameters in a diffusion model,” Appl. Opt. **41**, 3427–3435 (2002). [CrossRef] [PubMed]

11. S. Piazzola and B. Jenkins, “First-harmonic diffusion model for holographic grating formation in photopolymers,” J. Opt. Soc. Am. B **17**, 1147–1157 (2000). [CrossRef]

^{2}(again the point

*t*=0 was the time when exposure was stopped).

**81**, 5913–5923 (1997). [CrossRef]

**43**, 2900–2905 (2004). [CrossRef] [PubMed]

21. A. Veniaminov and E. Bartsch, “Diffusional enhancement of holograms: phenanthrenequinone in polycarbonate,” J. Opt. A: Pure Appl. Opt. **4**, 387–392 (2002). [CrossRef]

_{i}are diffusion times for the first and second diffusion processes and

*βi*are the stretching parameters and their deviations from unity are a measure of the heterogeneity of the characterized systems or processes. The curves presented on Fig.3 are fitted using Microcal Origin software applying the Levenberg–Marquardt method to minimize the chi-square value.

_{1}as a function of the square of spots radius. It is seen that a very good linear dependence has been obtained. From the slope of the linear fit a diffusion constant value of 4.2×10

^{-7}cm

^{2}/s was calculated. The calculated stretching parameters are

*β*

_{1}=1 for the increase in the profile and

*β*

_{2}=0.8 for the subsequent decrease indicating some heterogeneity of the second process.

### 3.2 Calculation of diffusion coefficient

8. G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. **41**, 1929–1939 (1994). [CrossRef]

*m*(

*x*,

*t*) is the monomer concentration,

*D*(

*x*,

*t*) is the diffusion coefficient and

*t*and

*x*are the time and spatial coordinates. In Eq. (5) the term associated with the polymerization has been omitted because we assumed that the polymerization stops shortly after exposure. Furthermore, because the growth of the profile is due to monomer diffusion, we can assume that the height of the profile

*h*(

*x*,

*t*) is proportional to the monomer concentration:

*m*

_{0}is the initial monomer concentration (spatially and time independent) and

*A*is the proportionality constant. Eq. (6) is well understandable especially at the center of the spot where accumulation of monomer leads to swelling. Because

*h*is measured in a small area around the center of the profile we can assume that

*D*is spatially independent. Then Eq. (5) and Eq. (6) lead to:

*h*are measured (Fig.2) we can calculate the partial derivatives in Eq. (7). The measured curves

*h*(

*t*) and

*h*(

*x*) were smoothed before the differentiation. A smooth curve

*h*(

*t*) was generated by fitting the experimental data using Eq. (4) as described above. The function,

*h*(

*x*), was smoothed using the Microcal Origin FFT filter for curve smoothing. The first derivative of

*h*with respect to the time

*t*and the second derivative of

*h*with respect to spatial coordinate

*x*were calculated from the measured time (Fig. 2(b)) and spatial (Fig. 2(a)) dependences of the profile, respectively, by averaging the slopes of two adjacent data points using the Microcal Origin Program. The diffusion coefficient is calculated from:

*t*=15,30…300s and

_{i}*x*is the centre of the profile.

_{c}*D*are presented in Fig. 4.

*D*, the intensity attenuation through the layer was calculated and is presented as an inset in Fig. 4. The value of the absorption coefficient used in the calculation is firstly determined from transmittance and reflectance measurements of the sample. It is seen that for 60µm thick layers the light intensity at the upper boundary is almost twice that at the lower. Having in mind that the polymerization rate increases with light intensity [8–11

8. G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. **41**, 1929–1939 (1994). [CrossRef]

22. R. Jallapuram, I. Naydenova, H. J. Byrne, S. Martin, R. Howard, and V. Toal, “Raman spectroscopy for the characterization of the polymerization rate in an acrylamide-based photopolymer,” Appl. Opt. **47**, 206–212 (2008). [CrossRef] [PubMed]

23. S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. Sheridan, “3 Dimensional analysis of holographic photopolymers based memories,” Opt. Express **13**, 3543–3557 (2005). [CrossRef] [PubMed]

24. S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, “Analysis of monomer diffusion in depth in photopolymer materials,” Opt. Commun. **274**, 43–49 (2007). [CrossRef]

*D*was calculated for each set of measurements. The obtained standard deviation from the mean value is less than 10%.

### 3.3 Intensity dependence of D

**41**, 1929–1939 (1994). [CrossRef]

22. R. Jallapuram, I. Naydenova, H. J. Byrne, S. Martin, R. Howard, and V. Toal, “Raman spectroscopy for the characterization of the polymerization rate in an acrylamide-based photopolymer,” Appl. Opt. **47**, 206–212 (2008). [CrossRef] [PubMed]

*D*is somewhat unexpected because if at higher intensity more polymer is formed, the density of the sample will increase and the diffusion will slow down. However, it has been established that higher intensity leads to the formation of shorter polymer chains [25]. Therefore, due to shorter polymer chains the sample illuminated at higher intensity could be less dense than a sample illuminated at lower intensity and the diffusion through it would be easier, that means the diffusion coefficient will be higher. A similar dependence of

*D*on the intensity is observed for the second process (decrease in the profile height). Having in mind that usually it is assumed that this process is polymer diffusion away from the illuminated area, [12

**43**, 2900–2905 (2004). [CrossRef] [PubMed]

*D*for higher intensity can be explained by greater mobility of the shorter polymer chains.

26. M. Toishi, T. Tanaka, and K. Watanabe, “Analysis of temperature change effects on hologram recording and a compensation method,” Opt. Rev. **15**, 1–8 (2008). [CrossRef]

*D*for higher intensity can be expected, especially for the first process. However, 120 s after the initial illumination (the second process), the temperature dependence of

*D*should be weaker than that for the first process and in fact no significant influence of the temperature on

*D*should be observed. To the contrary, our experimental results showed that for the second process the intensity dependence of

*D*is as pronounced as for the first process. This leads us to the conclusion that the first explanation of intensity dependence of

*D*is more likely.

### 3.4 Polymer density dependence

*D*using Eq. (8) (

*D*=5.3×10

^{-7}cm

^{2}/s) and the value from the slope of the curves of τ vs

*r*

^{2}(

*D*=4.2×10

*-7*cm

*2*/s) is obtained. Comparison with the values of monomer and polymer diffusion coefficients obtained from the post-exposure dynamics of the diffraction efficiencies of weak gratings [13] shows that Eq. (8) gives values about an order of magnitude higher. A possible reason may be that the method for calculation of

*D*presented here gives near-surface values of

*D*and some alteration of the surface may be expected compared to the volume. But we believe that the most probable reason of the observed discrepancies is the different wavelengths of initial illumination (554 nm in our study, compared to 532 nm in Ref. [13]). Even under the same conditions of initial exposure, the polymerization rates will be different due to different absorption coefficients of the sensitizing dye at these two wavelengths. Consequently, the degree of conversion of monomer to polymer will not be the same. This problem could be overcome if a narrow band filter with central wavelength of 532nm is used instead of 554nm filter.

## 4. Conclusion

*D*is simple and straightforward; no complicated multiparametric models or nonlinear fitting procedures are needed. Moreover, the diffusion coefficient is determined separately from the polymerization rate, eliminating the necessity for preliminary information and assumptions in the modeling of processes taking place in holographic recording in photopolymers. The calculated values for the diffusion coefficients are in very good agreement with the values obtained from the slope of the linear dependence of diffusion time on distance squared. Furthermore very good reproducibility is achieved. By varying the conditions of initial exposure, polymer density and intensity dependence of

*D*can be obtained. Despite the fact that the method gives the near-surface values of

*D*it could be successfully applied for comparative studies and we believe it will be useful in material science.

## Acknowledgments

## References and links

1. | T. J. Trout, J. J. Schmieg, W. Y. Gambogi, and A. M. Weber, “Optical photopolymers: Design and applications,” Adv. Mat. |

2. | A. Sullivan, M. Grabowski, and R. McLeod, “Three-dimensional direct-write lithography into photopolymer,” Appl. Opt. |

3. | S. Guntaka, V. Toal, and S. Martin, “Holographically recorded photopolymer diffractive optical element for holographic and electronic speckle-pattern Interferometry,” Appl. Opt. |

4. | H. J. Zhou, V. Morozov, and J. Neff, “Characterization of DuPont photopolymers in infrared light for free-space optical interconnects,” Appl. Opt. |

5. | H. Sherif, I Naydenova, S. Martin, C. McGinn, and V. Toal, “Characterization of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing,” J. Opt. A:Pure&Appl. Opt. |

6. | |

7. | |

8. | G. Zhao and P. Mouroulis, “Diffusion model of hologram formation in dry photopolymer materials,” J. Mod. Opt. |

9. | V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, “Quantitative model of volume hologram formation in photopolymers,” J. Appl. Phys. |

10. | V. Moreau, Y. Renotte, and Y. Lion, “Characterization of DuPont photopolymer: determination of kinetic parameters in a diffusion model,” Appl. Opt. |

11. | S. Piazzola and B. Jenkins, “First-harmonic diffusion model for holographic grating formation in photopolymers,” J. Opt. Soc. Am. B |

12. | I. Naydenova, R. Jallapuram, R. Howard, S. Martin, and V. Toal, “Investigation of the Diffusion Processes in a Self-Processing Acrylamide-Based Photopolymer System,” Appl. Opt. |

13. | S. Martin, I. Naydenova, R. Jallapuram, R. Howard, and V. Toal, “Two-way diffusion model for the recording mechanism in a self developing dry acrylamide photopolymer,” Proc. SPIE |

14. | S. Martin, C. A. Feely, and V. Toal, “Holographic recording characteristics of an acrylamide-based photopolymer,” Appl. Opt. |

15. | A. Havranek, M. Kveton, and J. Havrankova, “Polymer holography II - The theory of hologram growth. Polymer growth detected by holographic method,” Polymer Bulletin |

16. | C. Croutxe-Barghorn and D. J. Lougnot, “Use of self-processing dry photo-polymers for the generation of relief optical elements: a photochemical study,” Pure Appl. Opt. |

17. | J. Neumann, K. S. Wieking, and D. Kip, “Direct laser writing of surface reliefs in dry, self-developing photopolymer films,” Appl. Opt. |

18. | I. Naydenova, E. Mihaylova, S. Martin, and V. Toal, “Holographic patterning of acrylamide-based photopolymer surface,” Opt. Express |

19. | K. Pavani, I. Naydenova, S. Martin, and V. Toal, “Photoinduced surface relief studies in an acrylamide-based photopolymer,” J. Opt. A: Pure Appl. Opt. |

20. | W. J. Roff and J. R. Scott, |

21. | A. Veniaminov and E. Bartsch, “Diffusional enhancement of holograms: phenanthrenequinone in polycarbonate,” J. Opt. A: Pure Appl. Opt. |

22. | R. Jallapuram, I. Naydenova, H. J. Byrne, S. Martin, R. Howard, and V. Toal, “Raman spectroscopy for the characterization of the polymerization rate in an acrylamide-based photopolymer,” Appl. Opt. |

23. | S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. Sheridan, “3 Dimensional analysis of holographic photopolymers based memories,” Opt. Express |

24. | S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, “Analysis of monomer diffusion in depth in photopolymer materials,” Opt. Commun. |

25. | P. Munk and T. M. Aminabhavi, “Introduction to macromolecular science,” (Jonh Wiley & Sons, Inc., New York, 2002). |

26. | M. Toishi, T. Tanaka, and K. Watanabe, “Analysis of temperature change effects on hologram recording and a compensation method,” Opt. Rev. |

**OCIS Codes**

(090.0090) Holography : Holography

(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

(160.5470) Materials : Polymers

(180.3170) Microscopy : Interference microscopy

(290.1990) Scattering : Diffusion

**ToC Category:**

Materials

**History**

Original Manuscript: March 13, 2008

Revised Manuscript: May 22, 2008

Manuscript Accepted: May 22, 2008

Published: May 27, 2008

**Citation**

Tzwetanka Babeva, Izabela Naydenova, Suzanne Martin, and Vincent Toal, "Method for characterization of diffusion properties of photopolymerisable systems," Opt. Express **16**, 8487-8497 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8487

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### References

- T. J. Trout, J. J. Schmieg, W. Y. Gambogi, and A. M. Weber, "Optical photopolymers: Design and applications," Adv. Mater. 10, 1219-1224 (1998). [CrossRef]
- A. Sullivan, M. Grabowski, and R. McLeod, "Three-dimensional direct-write lithography into photopolymer," Appl. Opt. 46, 295-301 (2007). [CrossRef] [PubMed]
- S. Guntaka, V. Toal, and S. Martin, "Holographically recorded photopolymer diffractive optical element for holographic and electronic speckle-pattern Interferometry," Appl. Opt. 41, 7475-7479 (2002). [CrossRef] [PubMed]
- H. J. Zhou, V. Morozov, and J. Neff, "Characterization of DuPont photopolymers in infrared light for free-space optical interconnects," Appl. Opt. 34, 7457-7459 (1995). [CrossRef] [PubMed]
- H. Sherif, I. Naydenova, S. Martin, C. McGinn, and V. Toal, "Characterization of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing," J. Opt. A:Pure&Appl. Opt. 7, 255-261 (2005). [CrossRef]
- http://www.inphase-technologies.com/
- http://www.aprilisinc.com/
- G. Zhao and P. Mouroulis, "Diffusion model of hologram formation in dry photopolymer materials," J. Mod. Opt. 41, 1929-1939 (1994). [CrossRef]
- V. L. Colvin, R. G. Larson, A. L. Harris, and M. L. Schilling, "Quantitative model of volume hologram formation in photopolymers," J. Appl. Phys. 81, 5913-5923 (1997). [CrossRef]
- V. Moreau, Y. Renotte, and Y. Lion, "Characterization of DuPont photopolymer: determination of kinetic parameters in a diffusion model," Appl. Opt. 41, 3427-3435 (2002). [CrossRef] [PubMed]
- S. Piazzola and B. Jenkins, "First-harmonic diffusion model for holographic grating formation in photopolymers," J. Opt. Soc. Am. B 17, 1147-1157 (2000). [CrossRef]
- I. Naydenova, R. Jallapuram, R. Howard, S. Martin, and V. Toal, "Investigation of the Diffusion Processes in a Self-Processing Acrylamide-Based Photopolymer System," Appl. Opt. 43, 2900-2905 (2004). [CrossRef] [PubMed]
- S. Martin, I. Naydenova, R. Jallapuram, R. Howard, and V. Toal, "Two-way diffusion model for the recording mechanism in a self developing dry acrylamide photopolymer," Proc. SPIE 6252, 62525-625217 (2006).
- S. Martin, C. A. Feely, and V. Toal, "Holographic recording characteristics of an acrylamide-based photopolymer," Appl. Opt. 36, 5757-5768 (1997). [CrossRef] [PubMed]
- A. Havranek, M. Kveton, and J. Havrankova, "Polymer holography II - The theory of hologram growth. Polymer growth detected by holographic method," Polymer Bulletin 58, 261-269 (2007).
- C. Croutxe-Barghorn and D. J. Lougnot, "Use of self-processing dry photo-polymers for the generation of relief optical elements: a photochemical study," Pure Appl. Opt. 5, 811-827 (1996). [CrossRef]
- J. Neumann, K. S. Wieking, and D. Kip, "Direct laser writing of surface reliefs in dry, self-developing photopolymer films," Appl. Opt. 38, 5418-5421 (1999). [CrossRef]
- I. Naydenova, E. Mihaylova, S. Martin, and V. Toal, "Holographic patterning of acrylamide-based photopolymer surface," Opt. Express 13, 4878-4889 (2005). [CrossRef] [PubMed]
- K. Pavani, I. Naydenova, S. Martin, and V. Toal, "Photoinduced surface relief studies in an acrylamide-based photopolymer," J. Opt. A: Pure Appl. Opt. 9, 43-48 (2007). [CrossRef]
- W. J. Roff and J. R. Scott, Fibers, films, plastics and rubbers, a handbook of common polymers (Butterworths, London, 1971).
- A. Veniaminov and E. Bartsch, "Diffusional enhancement of holograms: phenanthrenequinone in polycarbonate," J. Opt. A: Pure Appl. Opt. 4, 387-392 (2002). [CrossRef]
- R. Jallapuram, I. Naydenova, H. J. Byrne, S. Martin, R. Howard, and V. Toal, "Raman spectroscopy for the characterization of the polymerization rate in an acrylamide-based photopolymer," Appl. Opt. 47, 206-212 (2008). [CrossRef] [PubMed]
- S. Gallego, M. Ortuño, C. Neipp, A. Márquez, A. Beléndez, I. Pascual, J. V. Kelly, and J. Sheridan, "3 Dimensional analysis of holographic photopolymers based memories," Opt. Express 13, 3543-3557 (2005). [CrossRef] [PubMed]
- S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, "Analysis of monomer diffusion in depth in photopolymer materials," Opt. Commun. 274, 43-49 (2007). [CrossRef]
- P. Munk and T. M. Aminabhavi, "Introduction to macromolecular science," (Jonh Wiley & Sons, Inc., New York, 2002).
- M. Toishi, T. Tanaka, and K. Watanabe, "Analysis of temperature change effects on hologram recording and a compensation method," Opt. Rev. 15, 1-8 (2008). [CrossRef]

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