research article paper on designing costless thz paper...

Research ArticlePaper on Designing Costless THz Paper Optics

A Siemion1 P Kostrowiecki-Lopata1 A Pindur1 P Zagrajek2 and M Sypek1

1Faculty of Physics Warsaw University of Technology 75 Koszykowa Str 00-662Warsaw Poland2Institute of Optoelectronics Military University of Technology 2 Kaliski Str 00-908Warsaw Poland

Correspondence should be addressed to A Siemion agnieszkaifpwedupl

Received 8 August 2016 Accepted 7 November 2016

Academic Editor Eric Freysz

Copyright copy 2016 A Siemion et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Designing diffractive optical elements is crucial for efficient development of THz techniquesHere we consider paper structures andwe analyze their advantages and disadvantages in fast prototyping The discussion about using material parameters like refractiveindex and absorption coefficient in designing diffractive optical elements is shownWe analyze the influence of phase stepmismatchof attenuation of real structure and of nonuniform illumination on the efficiency of the structure All these features result inworsening of the diffraction efficiency but they do not seem to have such significant influence as shadow effect introduced byfast varying zones Diffractive elements can be designed with very good accordance with experimental results which makes themideal for possible applications Paper optics scan be used more for fast prototyping nevertheless its performance can be increasedby placing it inside water protecting foil

1 Introduction

More andmore efficient emission of THz radiation is openingnew possibilities for security [1] noninvasive testing [2]material identification [3] and medical diagnosis [4] THzwaves are promising in detectingmetal objects hidden behindsomething like it takes place in case of brown-up or white-upduring landing of helicopters To efficiently use and transformthe THz radiation we can use beam shaping to form thedesired intensity pattern and elements gathering and focusingthe beam to significantly enhance the amount of radiationimpinging the detectorrsquos surface and assuring larger signaland therefore more efficient detection Moreover such opticscan significantly reduce optical cross-talk in the case ofmatrix of detectors

Mirrors used for THz beams can reflect the radiation andare wavelength independent but positioning of the system isnot easy and elements are rather expensive especially whenthey have more complicated shapes For diffractive elementsvarious structures complicated in shape are available (theycan be easily manufactured with different 3D printing tech-niques laser cutting or even with milling but only for axiallysymmetrical structures) Such elements strongly depend on

the design wavelength but this drawback can be suppressedby clever designing [5]

2 Materials for THz

Because of the fast development of THz technology it iscrucial to find newmaterials which will allow for easy manu-facturing of optical elements The question is what materialshould we use to manufacture diffractive objects for THzwaves The perfect material should be inexpensive and easyin processing and should possess good optical parameters Inorder to provide strong signal attenuation coefficient shouldbe low to prevent the structure from absorbing most of theincoming energy Refractive index should be more or lessconstant in whole used THz regionThere are manymaterialsfulfilling these requirements Themost frequently used mate-rials for fabricating THz components are Teflon TPX [6]Zeonex [7] TOPAS [8] polytetrafluoroethylene (PE) [9] andhigh-density polyethylene (HDPE) [10] Another materialis high-resistivity silicon [11] however more materials canbe used in manufacturing THz beam shaping objects forexample conductive polymers [12] metal [13 14] naturalstone [15] and metamaterials [16] It should be noticed that

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2016 Article ID 9615698 13 pageshttpdxdoiorg10115520169615698

2 Advances in Materials Science and Engineering

more and more 3D printed materials like polyamide 12 orother plastics [17 18] are used to manufacture diffractiveoptical elements Another attempt considers using paper forTHz beam shaping purposes [19 20]

The best solution is to find the material having therefractive index for particular design frequency in the 14ndash17range It results from the fact that for higher differenceof refractive index between air and used material (egair-silicone interface introduces the change of around 24while air-paper around 05) we will encounter high Fres-nel losses and therefore using some antireflection coatingsis recommended Nevertheless in case of frequently usedhemispherical lenses it is almost impossible to create goodand efficient antireflection coating due to the fact that thelight illuminates the lens from various angles In case of toosmall refractive index the structure is becoming thick whichsignificantly increases attenuation and independently shadoweffect [21ndash23]

It should be also noticed that not all materials are readyfor outdoor use In this case paper structures are rather for fastprototyping however we can use protecting foils to protectthem from humidity or rain

3 Designing DOEs

The functioning of diffractive optical elements can bedescribed by analogy to the diffractive grating In this kindof structures a part of the incident light is not changedand propagates in the same way after the object but someof the energy is redirected and forms diffraction ordersOn the contrary to refractive lenses which collects almost100 of the incident light in the focal spot (not takinginto account their attenuation) their diffractive counterpartsdo not have 100 efficiency directed into one particularorder In case of diffraction gratings depending on thestructure we can obtain different efficiency in different ordersby manipulating grating parameters such as fill factor orthicknesstransparency of the structure Diffractive opticalelements can introduce either changes of amplitude or phaseThe former will attenuate the incident radiation while thelatter may have theoretically even up to 100 of efficiency(with continuous phase profile) Considering the binarydiffraction grating the fill factor 119886 can be easily defined asthe fraction of the period of the diffraction grating that isfilled with the grating material (either changing amplitudeor phase) However for more complicated structures the fillfactor is not as clear in interpretation due to the fact that theshape the transparency the height of the structure or thewidth of the designed zones are variously changing

Therefore it is easy to define the diffraction efficiency forbinary phase grating in general case which can be calculatedusing formulas (1) [24] as follows

1205780 = 1 + 4119886[sin2 (1206012)]

120578119898 = 4sin2 (1206012)(120587119898)2 sin2 (120587119898119886)

(1)

where 119898 is the order of diffraction 120601 is the height of thephase step (a kind of the threshold level which should beequal to 120587 for the maximal possible diffraction efficiency)and 119886 is the fill factor Considering different structures thegeneral equation describing the amplitude coefficients ofthe expansion of the function describing the grating into aFourier series should be used as follows

1205780 = 1003816100381610038161003816119866010038161003816100381610038162 =1003816100381610038161003816100381610038161003816100381610038161119889 int1198892

minus1198892119891 (119909) 119889119909

1003816100381610038161003816100381610038161003816100381610038162

120578119898 = 100381610038161003816100381611986611989810038161003816100381610038162 =1003816100381610038161003816100381610038161003816100381610038161119889 int1198892

minus1198892119891 (119909) 119890minus2120587119894(119898119909119889)119889119909

1003816100381610038161003816100381610038161003816100381610038162

(2)

Therefore the exact theoretical calculation of diffraction effi-ciency is rather complicated and indirect for more advancedstructures However the estimation may be carried outbecause it is relatively easy to define it for simpler structurethat would correspond to the less efficient case of complicatedstructure

It should be underlined that fast changes of fill factor (likefor narrow zones whose width is lower than the thicknessof the structure) mostly introduce the decrease of efficiencyin the range of only few percentages Much more significantis the shadow effect [21] that can considerably decreasethe efficiency especially for kinoform structures (for binarystructures this effect is less important due to the smallerthickness of the structure)

Here we concentrated our research on paper struc-tures which are easy in fabrication very cost-efficient andfast in manufacturing There are two methods which areworth mentioning One of them is laser cutting [20] and itallows obtaining binary structures or eventually multistepphase structures (maximum 3-4 steps but it is wavelengthdependent and corresponds to diffractive zones widths) Thesmallest feature is limited by the kerf of the laser cutting(which is the gap resulting from the finite laser spot size)The second method is 3D printing based on cutting thepaper [25] In this manufacturing method it is possible toperform automatic manufacturing of kinoforms but its maindrawback is the need of the thin substrate (around 1-2-mm-thick) in order to get rid of local zero thickness and toguarantee proper stability of the structure [26] A classicalkinoform is a phase diffractive object which modulates thephase of incident light from the range 0ndash2120587 in a continuouswayWe can imagine that we take a refractive (thick) elementand slice it into layers changing phase from 0 to maximally2120587 and then remove all parts (blocks) introducing exactly2120587 shift In such way we will obtain a structure that is thinand has the same shape as refractive one but is formed withsteps having some maximal height (corresponding to the 2120587phase shift) whereas a high order kinoform (HOK) is anoptical structure that is made of zones similar to those intypical kinoform but having thickness corresponding to thephase shift of the multiplicity of 2120587 and therefore having alsodifferent widths In comparison to classical Fresnel lensessuch structure has better optical performance and is notsuffering from chromatic aberration like first-order kinoform

Advances in Materials Science and Engineering 3

[5] Therefore even using diffractive optics we can work inbroadband range

31 Influence of Refractive Index on Designed StructureRefractive index is very important for proper designing Inoptics the refractive index of the material dependent on thefrequency is mostly used however one can also use definingstructure parameters by its dielectric constant (if we assumesmall attenuation we can describe the refractive index asthe square root of dielectric constant) For phase diffractiveobjects the thickness of the structure corresponds to thephase change of the incident wave The relation between themaximum thicknesses ℎmax of the structure for introducingphase shift by 2120587 includes the influence of the used wave-length 120582 and refractive indices of the surrounding medium 1198990and of the structure 119899 described with the following equation

ℎmax = 120582119899 minus 1198990 (3)

That is why it is crucial to know the refractive index of theused material before designing the diffractive structure

32 Absorption Coefficient As it was mentioned it is veryimportant to know the optical parameters such as absorptioncoefficient and refractive index of the material (for design-ing diffractive optics we use values of 119899 and 120572 howeversometimes for THz and millimeter waves complex values areused) used to design the structure Both these values canbe precisely determined for many frequencies using TimeDomain Spectroscopy [27] Defining the refractive index iscrucial to match the proper height (and design appropriatestructure thickness) of the step of the designed structurewhile absorption coefficient tells us about losses introducedby the structure We can choose the material with smallestattenuation but in the designing process we cannot suppressthe influence of different absorption resulting from differentthicknesses of the structure We can simulate the result butsimilarly to the situation of nonuniform illumination wecannot change it

The easiest way to determine the absorption coefficientfor samples with known thickness (ℎ) is to measure theincident intensity of the light 119868119894 and transmitted intensity 119868119905Then the absorption coefficient can be calculated from thefollowing

119868119905 (119909) = 119868119894119890minus120572ℎ (4)

It allows us to determine how large will be the influence of theattenuation on our designed structure and what differencesof amplitude the structure will introduce However the casebecomes more complicated when the sample is not flat ornot homogeneous According to this fact it is difficult toestablish its thickness in every point In this case the simplestway to measure transmittance of the sample is by using thefollowing

119879 = 119868119905 cos (120579119905)119868119894 cos (120579119894) (5)

Table 1 Values of refractive indices and absorption coefficients forfrequency 03 THz (g) corresponds to samples with glue

Paper name ℎ [mm] plusmn 001mm 120572 [cmminus1] 119899 Δ119899 []3D orientA 397 2190 1399 mdash3D orientB 404 1694 1391 mdash3D orientC 414 1752 1395 mdashWhite 063 2122 1488 033White (g) 065 2024 1483Glossy 193 2076 1539 033Glossy (g) 194 2378 1544Black 226 2529 1577 031Black (g) 233 2368 1572Gray 175 2153 1546 037Gray (g) 177 1852 1552Crossed 067 2458 1500 100Crossed (g) 069 2121 1515Green 262 2037 1436Green (g) 262 2029 1434 014Green (g) + food foil 269 2008 1427 058Green (g) + office foil 271 2071 1431 031Green (g) + thick foil 270 2058 1437 011

where 120579119894 and 120579119905 are the angle of incidence and the angle ofrefraction respectively Both are measured according to thenormal to the surface Then we can make transmission mapsand verify what is the influence of variable attenuation on thedesigned structure

Nevertheless the thickness of the structure should berelatively small to enable efficient performance and theproper material should be used

In reality we must always assume that we are dealingwith amplitude and phase structures whose transmittance isdescribed with the following equation

119879 = 119860 (119909 119910) 119890119894120593(119909119910) (6)

So even if we are designing only phase structure wemust dealwith its amplitude contribution (due to the absorption of theused material)

33 Analyzed Papers Because there are a lot of differentkinds of papers available on the market it is possible tochoose the best one in terms of properties such as absorptioncoefficient and refractive index but also stiffness and othercrucial parameters We have examined some samples thatare listed in Table 1 and their values of refractive indicesand absorption coefficients for the frequency correspondingto the design wavelength (03 THz) are determined Table 1contains the name of each paper the thickness of the sample(measured with the digital micrometer screw with accuracy0001mm but taking into account flexibility of the materialwe assumed that the accuracy was 001mm) its absorptioncoefficient and refractive indexThe last column includes thedifference between the refractive indices of the paper withand without glue (given in percent) that shows that using gluedoes only slightly change paper parameters


The efficient numerical simulation which is consistentwith experimental results requires initial determinationof parameters of used material like refractive index andabsorption coefficient Therefore different paper sampleswere investigated by means of Teraview TPS Spectra 3000spectrometer THz optical setup was used in the transmissionmode and allowed determining paper material parametersfor the available part of THz frequency range Measurementswere performed in humidity controlled environment (driedair with the humidity not exceeding 05) The aging ofpaper does not influence the measurements during few yearsperiodThe described green paper was verified in 2011 for thefirst time [20] and now the new green paper and the old onehave same optical properties

First group of papers are (3D orientA 3D orientB and3D orientC) manufactured by 3D printing technique (McorIRIS printer [25]) from Xerox white paper with paper sub-stance (grammage) of 80 (gm2) Due to the manufacturingprocess they are already glued but samples have differentorientation of paper layers which changes their attenuationcoefficient The refractive index values are relatively the same(change smaller than 06)The orientation described here isthe sequence of gluing and cutting paper sheets in 3Dprintingtechnique which should not introduce birefringence

The rest of the sampleswere analyzed in twodifferent con-figurations layers of paper stacked on each otherwithout andwith adhesive bonding (3M Display mount glue) In Table 1we described optical parameters of different papers withabbreviated names and here we will give more details aboutthem Papers 3D orient were already described (Xerox whitepaper 80 (gm2)) White paper is commercially availableLyreco white paper with grammage also 80 (gm2) Glossyis Sirio Pearl paper manufactured by Fedrigoni in Ice Whitecolor with grammage 300 (gm2) Black is Burano papermanufactured by Favini in Nero color with grammage 320(gm2) Gray is cardboard folder manufactured by HamelinTop 2000 inWhite color with grammage 350 (gm2) Crossedis notebook squared paper manufactured by Basic in Whitecolor Green is Curious Metallics paper from Arjo Wiggins inJaspis color and 300 (gm2) Furthermore for green paper(which was used to create diffractive lens [28]) additionalmeasurements were carried out for different types of foilsthat could be used to create hermetic seals on the paper (nul-lifying the effect of humidity) As we can see the most similarvalues of both compared parameters have green paper mea-surements for all TDS frequency range are shown in Figure 1

For green paper both refractive index and absorptioncoefficient curves are smooth (Figure 2) When we assumethat paper is not resistant to water we can imagine puttingsuch structures into foil and sealing it inside Thereforewe examined the influence of adding the foil on values ofrefractive index and absorption coefficient All values differedless than 06 and both the shape of the curve and itstendency did not change This difference of refractive indicesis mostly the result of changing the thickness of the analyzedstructures (foil is almost transparent for THz radiation sopaper sample with added foil layers has bigger thicknessbut its attenuation remains more or less the same) In case

135

14

145

15

155

Refr

activ

e ind

ex

Absorption coefficientrefractive index

Green paperGreen paper with glueGreen paper with glue in food foilGreen paper with glue in office foilGreen paper with glue in thick foil

03 05 07 09 11 13 1501Frequency (THz)

0

4

8

12

16

20

Abso

rptio

n co

effici

ent (

cmminus1)

Figure 1 Absorption coefficient (dotted lines) and refractive index(full lines) curves for green paper with different additions

135

145

155

165

175

Refr

activ

e ind

ex


Black paperBlack paper with glue

03 05 07 09 11 13 1501Frequency (THz)

0

4

8

12

16

20

Abso

rptio

n co

effici

ent (

cmminus1)

Figure 2 Absorption coefficient (dotted lines) and refractive index(full lines) curves for black paper with and without glue

Table 2 The variation of the refractive index and the absorptioncoefficient for 03 THz for green paper with determined inaccuracy

Refractive index 119899 Absorption coefficient 120572 [cmminus1]1432 plusmn 0050 (35) 2040 plusmn 0032 (16)

of absorption coefficient there is no visible difference fordesign wavelength of 1mm (corresponding to 03 THz) Thevariation of refractive index and absorption coefficient aregathered and we determined one value with its inaccuracy forboth parameters which are shown in Table 2


(a) (b)

Figure 3 The phase distribution of the ideal diffractive kinoform (a) and binary (b) lens structure designed for the plane wave illuminationwhere white areas introduce 2120587 (a) and 120587 (b) phase shift and black do not change the phase

For higher frequencies (gt07 THz) absorption coefficientsfor different samples of green paper with foil start varyingfrom each other However it is important to remember thatthe higher the frequency is (around 15 THz and higher) themore noisy the absorption curve becomes thus the best mea-surements are conducted for lower frequencies Althoughthere is a possibility to measure absorption coefficient andrefractive index for frequencies higher than 07 THz wemustrealize that for this range these are only amplitude structures(due to the high attenuation) For higher frequencies it isadvisable to use other materials as phase structures whilefor lower frequencies the paper seems to be good materialTherefore due to the growing attenuation of paper for higherfrequencies we decided to use 03 THz which correspondsto the DWL = 1mm Such radiation can be used in THzscanning as we had already demonstrated but finally usingstructure from polyamide [29]

In case of paper structures consisting of more than onelayer (to assure proper height of the step) we must ensurepropermanufacturing in case of geometry and gluing to avoidunwanted effects resulting from spurious air layers betweenpaper layers Such phenomenon may be observed for blackpaper shown in Figure 2

It can be seen that for black paper there is significantdifference between two investigated configurations (with andwithout glue) This effect is present in both refractive indexand absorption coefficient curves (Figure 3) in the form offollowing peaks appearing for multiplicities of first frequency(around 02 THz) Frequencies for which characteristic peaksappear are as follows 021 044 068 and 091 THz It canbe easily noticed that structure without adhesive bondingacts similarly to Fabry-Perot resonator which is reflectingresonant frequencies whereas for glued structure this effectdisappears We do not know if the attenuated frequenciesare reflected back from the paper sample or attenuated andfor that reason some additional measurements should beperformed but since we want to avoid this effect we will notcontinue these considerations

4 Exemplary Structure

To demonstrate the applicability of the paper for designingdiffractive structures a toroidal lens was made from oneof the tested papers [26] The simulations were carried outfor the optical setup used in the experiment and shown inFigure 11

The toroidal lens instead of focusing light in one focalpoint like normal lens forms a ring with predefined diameterin the focal plane In an ideal case the diffractive structurewasdesigned in the form of kinoform having continuous phasechanges distribution and no attenuation which is shown inFigure 3

For the simplicity we manufactured the structure by lasercutting therefore we used the binary phase element whichcontains the correcting structure for the divergent wavefrontcoming from the pinhole The phase distribution of thedesigned element assuming the illumination from a pinholeis shown in Figure 4

Such structure should redirect the incident light in thelight ring in the focal plane Unfortunately in real caseit is almost impossible to create perfect kinoforms whichwould introduce only well-adjusted phase change withoutany attenuation Hence in order to facilitate manufacturingthe designed structure was recalculated into binary structureusing paper as a material (obtaining good results means thepossibility to manufacture paper DOE using laser cuttingor 3D printing techniques) Another problem is that it isimpossible to create structures ldquohanging in airrdquo Accordingto this inconvenience all manufactured binary structurespossess additional supporting bars or additional substratelayer Those reinforcements introduce some distortions inobtained energy distributions which can be seen as brightspots around the ring but they introduce less attenuation incomparison with additional layer of material

The manufactured structure was scanned in order tocarry out simulations for toroidal diffractive lens with addi-tional reinforcements (Figure 5)


50mm

100mm

Figure 4 The phase distribution of the ideal diffractive lens stru-cture where white areas introduce 120587 phase shift and black do notchange the phase

50mm

100mm

Figure 5The phase distribution of the designed and manufactureddiffractive lens structure (scanned) where white areas introduce 120587phase shift and black do not change the phase

5 Simulations

Simulations were performed by means of modified convo-lution method [30 31] on 4096119901119909 times 4096119901119909 matrices withsampling 50 times 50 120583m2The tested structure was designed forwavelength 120582 = 1mm which corresponds to the frequency03THz The designed lens had focal length 119891 = 100mmand was illuminated with divergent wave coming from thepinhole (25mm diameter) The pinhole was placed 300mmbefore the structure and the resulting wave illuminated mostof the structure almost uniformly

Here we want to carry out simulations showing theinfluence of manufacturing problems on obtained results andthe possibility of simulating different real conditions mostlypresent in experimental setups

Two types of input data were prepared for simulationsideal and scanned diffractive element shown in Figures 4and 5 First structure is an ideal representation of designeddiffractive lens-like structure whereas the second one is thescanned image of real manufactured object The differencebetween those two structures lies in the existence of suspend-ing bars which are required to keep different phase changingareas together

Three simulations were done for these two objects oneconsidering the possibility of manufacturing not-exact phasestep height (Figures 6 and 7) second assuming the attenu-ation of the elements made from paper (Figures 8 and 9)

and third taking into account that the beam illuminatingthe structure has Gaussian-like intensity shape with differentdiameters (which corresponds to the nonuniform illumina-tion Figure 10)

In the first series of simulations the influence of phasechange mismatch was checked This was done by changingthe phase delay introduced by the phase object In real caseintroduced phase delay corresponds to the thickness of theobject thus this simulation allows investigating the effectof manufacturing process precision or rather its imprecision(regarding not matched thickness) on the obtained efficiencyHere we assume uniform amplitude over the whole structureand we analyze only the varying value of the phase step value120601 corresponding to the height of the phase step introducing 120587phase shift (Figure 6)The intensity distributions of simulatedstructures are shown in Figures 6(a)ndash6(i)

Next we assume the same uniform amplitude over thewhole structure with varying phase step value 120601 for themanufactured structured After preparing the design of thestructure with supporting bars it was manufactured bylaser cutting and then scanned to perform the simulationsverifying its correctness The results obtained in Figure 7show intensity distributions for the scanned structure fordifferent phase delays that correspond to the one calculatedfor the ideal structure (Figure 6)

Results show that due to the phasemismatch the uniformintensity distribution inside the circle changes and we canobserve either bright or dark dots in the middle (dependingon the phase mismatch) that do not appear for the idealtoroidal lens This effect is almost not observable in simu-lation results for scanned object thus it is possible to saythat small phase delay mismatching is not a crucial factor inproper functioning of the diffractive lens Simulation resultsfor scanned object also reveal the fact that more energy isfocused in particular points on the ring Those ldquodefectsrdquo arecaused by existence of suspending bars

The second simulation was conducted in order to inves-tigate how attenuationabsorption of paper affected outputfocal curve of the diffractive lens This was done by changingthe attenuation of the structure in regions where phasewas changed under the assumption of structure uniformity(Figure 8)These regions had lower amplitude in comparisonwith regions only with air (having 119860 = 1)

These intensity distributions do not vary in shape andthe difference is hard to notice (Figure 8) In case of scannedstructure simulation the obtained intensity distributions arealso very similar (Figure 9)

Due to the fact that there are no real visible differencesbetween simulation results for different attenuations of thestructure material we performed the quantitative compari-son As it can be seen the attenuation does not significantlyaffect the way lens works However it introduces changes inthe amount of focused light which can be seen from integralvalues presented in Table 3 For each intensity distribution wehave calculate the total intensity of all pixels forming focalcurve and then normalized it to the value of ideal structurewithout assumed attenuation (like in Figure 8(c)) which wasalso the maximal value for all cases


Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 03 (b) 120601 = 05 (c) 120601 = 07

(d) 120601 = 09 (e) 120601 = 10 (f) 120601 = 11

(g) 120601 = 13 (h) 120601 = 15 (i) 120601 = 16

Figure 6The simulation parameters (amplitude and phase diagrams together with the structurersquos phase distribution) Intensity distributions(simulation results) for different phase mismatch for ideal diffractive lens Simulations were conducted for introduced phase delays as follows03 05 07 09 10 11 13 15 and 16 shown in (a)ndash(i) respectively


Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 08 (b) 120601 = 085 (c) 120601 = 09

(d) 120601 = 095 (e) 120601 = 10 (f) 120601 = 105

(g) 120601 = 11 (h) 120601 = 115 (i) 120601 = 12

Figure 7The simulation parameters (amplitude and phase diagrams together with the structurersquos phase distribution) Intensity distributions(simulation results) for different phase mismatch for scanned structure Simulations were conducted for introduced phase delay as follows08 085 09 095 10 105 11 115 and 12 shown in (a)ndash(i) respectively


Amp

1

A

0 x

Pha

0 x

(a) A = 08 (b)A = 09 (c) A = 10

120587

Figure 8The simulation parameters (amplitude and phase diagrams together with the structurersquos phase distribution) Intensity distributions(simulation results) for different material attenuation for ideal lens Simulations were conducted for material attenuation values (10 valuecorresponds to no attenuation situation) as follows 08 09 and 10 shown in (a)ndash(c) respectively

Amp

1

A

0 x

Pha

0 x

120587

(a) A = 08 (b)A = 09 (c) A = 10

Figure 9The simulation parameters (amplitude and phase diagrams together with the structurersquos phase distribution) Intensity distributions(simulation results) for different material attenuation for scanned lens Simulations were conducted for material attenuation values (10 valuecorresponds to no attenuation situation) as follows 08 09 and 10 shown in (a)ndash(c) respectively


Amp

1

0

w

x

Pha

0 x

120587

(d) w = 40mm (e) w = 50mm (f) w = 60mm

(b) w = 20mm (c) w = 30mm(a) Plane wave

Figure 10The simulation parameters (amplitude and phase diagrams together with the structurersquos phase distribution) Intensity distributions(simulation results) for different lens illumination Diffractive structures were illuminated with Gaussian beams with different waist values119908(in mm) as follows 20 30 40 50 and 60 shown in (b)ndash(f) respectively In case of sufficient illumination (plane wave) (a)

Now the difference is clearly seen The ideal structurehas 15 less energy in the focal plane when we assumed theamplitude in the paper region equal to 08 and not to 1 Forscanned structure we can see significant decrease of the totalintensity in the focal plane in comparison with ideal lens Itis caused mainly by the intensity disturbances introduced bysupporting barsThey were designed as radial lines which canbe without problems replaced with random distribution ofbars It would probably lower the overall intensity but therewould not be ldquodefectsrdquo visible now in the form of bright dotsin the ring

In most cases when we design diffractive structure weassume uniform illumination (plane wave) Unfortunately inreality it is not possible to obtain perfectly uniform illumi-

Table 3 Collected light according to value of the integral over thewhole image

Total intensity [au] 119860 = 08 (a) 119860 = 09 (b) 119860 = 1 (c)Ideal structure 085 093 100Scanned structure 055 060 065

nation We cannot simply change the shape of the beam butwe can simulate the influence of those irregularities

Third comparison was carried out in order to analyze theeffect of illumination of the designed lens with beam sizedifferent from lens diameter This was done for illuminationwith Gaussian-like beam having different waist values 119908


Examined lens

Detector

Converging lens f = 75mm

Pinhole d = 25mm

(a)

Yax

is (m

m)

X axis (mm)In

tens

ity (a

u)

110

3070 80 90 100 110 120 130 140 150

40

50

60

70

80

90

100

0

0002

0004

0006

0008

001

0012

0014

(b)

Figure 11 The experimental setup (a) and the intensity distribution registered in the focal plane (b)

Results clearly show that illumination of diffractive lenshas a crucial impact on the functionality of the structure Lensilluminated with smaller beam does not work as designed Itis caused by the fact that only part of the functioning area isilluminated thus only part of it is working For insufficientdiameter of the illuminating beam (like in Figure 10(b)) weeven cannot see the focusing into a circle With the increaseof illuminated area the diffractive structure starts to operateas it was designed For Gaussian beam with waist value biggerthan the diameter of the lens there is no visible change asthe structure is fully illuminated Overall illumination is acrucial factor for diffractive elements to work properly andmoreover it may be inferred that the proper illumination ofthe structure is more crucial than the exact values of thestructure thickness considering variable attenuation

6 Manufactured Structure-Results

According to the results obtained from simulations theexperimental evaluationwas carried out To test the structuresimple setupwas used (Figure 11) based on the Schottky diodeas a source and semiconductor transistor mounted on 119883119884119885

stage as the movable detector In order to ensure as uniformas possible illumination of the structure the THz wavefrontfrom the source was modified with converging lens (119891 =75mm) and a pinhole (119889 = 25mm) The divergence of thebeam was corrected by the designed structure and it focusedthe radiation 100mm after the structure (in the focal plane)The experimental setup is illustrated in Figure 11(a) togetherwith the registered amplitude distribution recalculated theintensity

The experimentally obtained result (Figure 11) prove thatdesigned and manufactured toroidal diffractive lens-likestructure can be used in order to modify the THz wave-front To show the good accordance between the theoreticalsimulation and experimental evaluation we have shownthe experimental distribution with simulation of scannedstructure and ideal structure in Figure 12

Simulations conducted for scanned structure (Figure12(b)) are giving almost the same shape as obtained inthe experiment (Figure 12(a)) What is worth mentioningis the fact that real focal plane was created at designeddistanceThis conformity is important for further attempts indesigning new optical structures for particular applications


(a) (b) (c)

Figure 12 Experimental results (a) compared to simulation results of scanned structure (b) and ideal case (c)

The experimental evaluation shows that with the knowledgeabout material which was used for manufacturing the struc-ture it is possible to perform simulations before actuallyproducing desired objectThanks to that it is possible to avoidproduction of many structures with bad parameters and thatopens new possibilities for bigger control over the THz beam

7 Conclusions

Paper occurs to be very good material for THz radiationManufacturing paper optical elements is cheap and fast thereare two simple methods which allow producing good qualitydiffractive structures Simulations carried out by means ofmodified convolution method allow properly foreseeing thebehavior of the radiation It was possible to obtain greataccordance betweennumerical simulations and experimentalevaluation However it is crucial to know the parameters ofthe used material before performing the simulations It wasproven that using adhesive bonding allows creating structuresfrom multiple layers of paper without resonating effects Theaddition of glue not always improves the efficiency but for thecase of arising resonant frequencies can significantly help tosuppress this unwanted effect

Moreover we suggest using suspension bars in randomplaces to suppress their influence on the intensity distributionin the focal plane of the designed element

Using paper as material for designing and manufacturingdiffractive elements allows fast prototyping and according toobtained results such structures can successfully modify theTHzwavefront What ismore paper structures are cheap andcan be used also to manufacture different optical elements[32]

Here we described manufacturing of optical element forTHz radiation from paper and the example of toroidal binarystructure focusing in a focal circle However optical struc-tures can bemanufactured frompaper with continuous phaseprofile (like kinoform structures) by 3D printer [25] whichwas demonstrated and compared in [26] even though the 3Dprinted lens must have substrate layer the kinoform structurehas bigger efficiency than the binary lens manufactured fromgreen paper described here

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was partially supported by National Center ofResearch and Development (NCBR) Grant LIDER020319L-513NCBR2014 The authors would like to thank DrNorbert Palka from Institute of Optoelectronics of MilitaryUniversity of Technology for the possibility of performingthemeasurements in Laboratory of Terahertz TechniqueTheauthors would also like to thank the Orteh Company forproviding LS 60 Software used for designing and modelingdiffractive optical elements

References

[1] N Palka ldquoIdentification of concealed materials includingexplosives by terahertz reflection spectroscopyrdquo Optical Engi-neering vol 53 no 3 Article ID 031202 2014

[2] N Palka and D Miedzinska ldquoDetailed non-destructive evalu-ation of UHMWPE composites in the terahertz rangerdquo Opticaland Quantum Electronics vol 46 no 4 pp 515ndash525 2014

[3] V A Trofimov and S A Varentsova ldquoAbout efficiency ofidentification of materials using spectrumdynamics ofmediumresponse under the action of THz radiationrdquo in TerahertzPhysics Devices and Systems III Advanced Applications inIndustry and Defense vol 7311 of Proceedings of SPIE p 73110UOrlando Fla USA April 2009

[4] J-H Son Terahertz Biomedical Science amp Tehcnology CRCPress Boca Raton Fla USA 2014

[5] J Suszek AM Siemion N Blocki et al ldquoHigh order kinoformsas a broadband achromatic diffractive optics for terahertzbeamsrdquo Optics Express vol 22 no 3 pp 3137ndash3144 2014

[6] httpwwwtydexopticscompdfTHz Materialspdf[7] httpwwwzeonexcomopticsaspx[8] S BuschMWeidenbach J C Balzer andMKoch ldquoTHzoptics

3D printed with TOPASrdquo Journal of Infrared Millimeter andTerahertz Waves vol 37 no 4 pp 303ndash307 2016

[9] J RMiddendorfDA LeMasterMZarepoor andER BrownldquoDesign of multi-order diffractive THz lensesrdquo in Proceedings


of the 37th International Conference on Infrared Millimeter andTerahertz Waves (IRMMW-THz rsquo12) pp 23ndash28 THz WavesWollongong Australia September 2012

[10] M Sypek M Makowski E Herault et al ldquoHighly efficientbroadband double-sided Fresnel lens for THz rangerdquo OpticsLetters vol 37 no 12 pp 2214ndash2216 2012

[11] E DWalsby S M Durbin D R S Cumming and R J BlaikieldquoAnalysis of silicon terahertz diffractive opticsrdquo Current AppliedPhysics vol 4 no 2ndash4 pp 102ndash105 2004

[12] B S-Y Ung BWeng R Shepherd D Abbott andC FumeauxldquoInkjet printed conductive polymer-based beam-splitters forterahertz applicationsrdquo Optical Materials Express vol 3 no 9pp 1242ndash1249 2013

[13] A Siemion A Siemion M Makowski et al ldquoOff-axis metallicdiffractive lens for terahertz beamsrdquo Optics Letters vol 36 no11 pp 1960ndash1962 2011

[14] E Herault J-L Coutaz A Siemion A Siemion M MakowskiandM Sypek ldquoPrism-like behavior at terahertz frequencies of a2D metallic grid with a varying periodicityrdquo Journal of InfraredMillimeter and Terahertz Waves vol 32 no 4 pp 403ndash4062011

[15] D Han K Lee J Lim S S Hong Y K Kim and J AhnldquoTerahertz lens made out of natural stonerdquo Applied Optics vol52 no 36 pp 8670ndash8675 2013

[16] D Hu G Moreno X Wang et al ldquoDispersion characteristic ofultrathin terahertz planar lenses based on metasurfacerdquo OpticsCommunications vol 322 pp 164ndash168 2014

[17] S F Busch M Weidenbach M Fey F Schafer T Probst andM Koch ldquoOptical properties of 3Dprintable plastics in the THzregime and their application for 3D printed THz opticsrdquo Journalof Infrared Millimeter and Terahertz Waves vol 35 no 12 pp993ndash997 2014

[18] A Siemion J Suszek M Sypek et al ldquoTHz characterization ofselected 3D-printing materialsrdquo in Proceedings of the 8th THzDays Areches-Beaufort France 2015

[19] B Scherger M Scheller N Vieweg S T Cundiff andM KochldquoPaper terahertz wave platesrdquo Optics Express vol 19 no 25 pp24884ndash24889 2011

[20] A Siemion A Siemion M Makowski et al ldquoDiffractive paperlens for terahertz opticsrdquoOptics Letters vol 37 no 20 pp 4320ndash4322 2012

[21] J Suszek M Sypek M Makowski et al ldquoEvaluation of theshadow effect in terahertz kinoform gratingsrdquo Optics Lettersvol 38 no 9 pp 1464ndash1466 2013

[22] P Lalanne S Astilean P Chavel E Cambril and H LaunoisldquoDesign and fabrication of blazed binary diffractive elementswith sampling periods smaller than the structural cutoffrdquoJournal of the Optical Society of America A vol 16 no 5 pp1143ndash1156 1999

[23] D W Prather D Pustai and S Shi ldquoPerformance of multileveldiffractive lenses as a function of f-numberrdquoApplied Optics vol40 no 2 pp 207ndash210 2001

[24] J W Goodman Introduction to Fourier Optics McGraw-HillNew York NY USA 2004

[25] httpmcortechnologiescom3d-printersiris[26] M Rachon K Wegrzynska M Sypek et al ldquoEfficiency of

THz paper optical elements depending on their type andmanufacturing techniquesrdquo OSA Technical Digest 2015

[27] L Duvillaret F Garet and J-L Coutaz ldquoA reliable methodfor extraction of material parameters in terahertz time-domainspectroscopyrdquo IEEE Journal on Selected Topics in QuantumElectronics vol 2 no 3 pp 739ndash745 1996

[28] A Siemion A Siemion J Suszek et al ldquoTHz Beam ShapingBased on Paper Diffractive Opticsrdquo IEEE Transactions onTerahertz Science and Technology vol 6 no 4 pp 568ndash5752016

[29] J Suszek A Siemion D Coquillat et al ldquo3D printed flatoptics and InP heterojunction bipolar transistor based-detectorfor THz imagingrdquo in Proceedings of the 40th InternationalConference on InfraredMillimeter andTerahertzWaves pp 1ndash22015

[30] M Sypek ldquoLight propagation in the Fresnel region Newnumerical approachrdquo Optics Communications vol 116 no 1ndash3pp 43ndash48 1995

[31] M Sypek C Prokopowicz andMGorecki ldquoImagemultiplyingand high-frequency oscillations effects in the Fresnel regionlight propagation simulationrdquo Optical Engineering vol 42 no11 pp 3158ndash3164 2003


Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


more and more 3D printed materials like polyamide 12 orother plastics [17 18] are used to manufacture diffractiveoptical elements Another attempt considers using paper forTHz beam shaping purposes [19 20]

The best solution is to find the material having therefractive index for particular design frequency in the 14ndash17range It results from the fact that for higher differenceof refractive index between air and used material (egair-silicone interface introduces the change of around 24while air-paper around 05) we will encounter high Fres-nel losses and therefore using some antireflection coatingsis recommended Nevertheless in case of frequently usedhemispherical lenses it is almost impossible to create goodand efficient antireflection coating due to the fact that thelight illuminates the lens from various angles In case of toosmall refractive index the structure is becoming thick whichsignificantly increases attenuation and independently shadoweffect [21ndash23]

It should be also noticed that not all materials are readyfor outdoor use In this case paper structures are rather for fastprototyping however we can use protecting foils to protectthem from humidity or rain

3 Designing DOEs

The functioning of diffractive optical elements can bedescribed by analogy to the diffractive grating In this kindof structures a part of the incident light is not changedand propagates in the same way after the object but someof the energy is redirected and forms diffraction ordersOn the contrary to refractive lenses which collects almost100 of the incident light in the focal spot (not takinginto account their attenuation) their diffractive counterpartsdo not have 100 efficiency directed into one particularorder In case of diffraction gratings depending on thestructure we can obtain different efficiency in different ordersby manipulating grating parameters such as fill factor orthicknesstransparency of the structure Diffractive opticalelements can introduce either changes of amplitude or phaseThe former will attenuate the incident radiation while thelatter may have theoretically even up to 100 of efficiency(with continuous phase profile) Considering the binarydiffraction grating the fill factor 119886 can be easily defined asthe fraction of the period of the diffraction grating that isfilled with the grating material (either changing amplitudeor phase) However for more complicated structures the fillfactor is not as clear in interpretation due to the fact that theshape the transparency the height of the structure or thewidth of the designed zones are variously changing

Therefore it is easy to define the diffraction efficiency forbinary phase grating in general case which can be calculatedusing formulas (1) [24] as follows

1205780 = 1 + 4119886[sin2 (1206012)]

120578119898 = 4sin2 (1206012)(120587119898)2 sin2 (120587119898119886)

(1)

where 119898 is the order of diffraction 120601 is the height of thephase step (a kind of the threshold level which should beequal to 120587 for the maximal possible diffraction efficiency)and 119886 is the fill factor Considering different structures thegeneral equation describing the amplitude coefficients ofthe expansion of the function describing the grating into aFourier series should be used as follows

1205780 = 1003816100381610038161003816119866010038161003816100381610038162 =1003816100381610038161003816100381610038161003816100381610038161119889 int1198892

minus1198892119891 (119909) 119889119909

1003816100381610038161003816100381610038161003816100381610038162

120578119898 = 100381610038161003816100381611986611989810038161003816100381610038162 =1003816100381610038161003816100381610038161003816100381610038161119889 int1198892

minus1198892119891 (119909) 119890minus2120587119894(119898119909119889)119889119909

1003816100381610038161003816100381610038161003816100381610038162

(2)

Therefore the exact theoretical calculation of diffraction effi-ciency is rather complicated and indirect for more advancedstructures However the estimation may be carried outbecause it is relatively easy to define it for simpler structurethat would correspond to the less efficient case of complicatedstructure

It should be underlined that fast changes of fill factor (likefor narrow zones whose width is lower than the thicknessof the structure) mostly introduce the decrease of efficiencyin the range of only few percentages Much more significantis the shadow effect [21] that can considerably decreasethe efficiency especially for kinoform structures (for binarystructures this effect is less important due to the smallerthickness of the structure)

Here we concentrated our research on paper struc-tures which are easy in fabrication very cost-efficient andfast in manufacturing There are two methods which areworth mentioning One of them is laser cutting [20] and itallows obtaining binary structures or eventually multistepphase structures (maximum 3-4 steps but it is wavelengthdependent and corresponds to diffractive zones widths) Thesmallest feature is limited by the kerf of the laser cutting(which is the gap resulting from the finite laser spot size)The second method is 3D printing based on cutting thepaper [25] In this manufacturing method it is possible toperform automatic manufacturing of kinoforms but its maindrawback is the need of the thin substrate (around 1-2-mm-thick) in order to get rid of local zero thickness and toguarantee proper stability of the structure [26] A classicalkinoform is a phase diffractive object which modulates thephase of incident light from the range 0ndash2120587 in a continuouswayWe can imagine that we take a refractive (thick) elementand slice it into layers changing phase from 0 to maximally2120587 and then remove all parts (blocks) introducing exactly2120587 shift In such way we will obtain a structure that is thinand has the same shape as refractive one but is formed withsteps having some maximal height (corresponding to the 2120587phase shift) whereas a high order kinoform (HOK) is anoptical structure that is made of zones similar to those intypical kinoform but having thickness corresponding to thephase shift of the multiplicity of 2120587 and therefore having alsodifferent widths In comparison to classical Fresnel lensessuch structure has better optical performance and is notsuffering from chromatic aberration like first-order kinoform




ℎmax = 120582119899 minus 1198990 (3)




119868119905 (119909) = 119868119894119890minus120572ℎ (4)


119879 = 119868119905 cos (120579119905)119868119894 cos (120579119894) (5)






119879 = 119860 (119909 119910) 119890119894120593(119909119910) (6)








135

14

145

15

155

Refr

activ

e ind

ex



03 05 07 09 11 13 1501Frequency (THz)

0

4

8

12

16

20

Abso

rptio

n co

effici

ent (

cmminus1)


135

145

155

165

175

Refr

activ

e ind

ex



03 05 07 09 11 13 1501Frequency (THz)

0

4

8

12

16

20

Abso

rptio

n co

effici

ent (

cmminus1)






(a) (b)












50mm

100mm


50mm

100mm


5 Simulations













Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 03 (b) 120601 = 05 (c) 120601 = 07

(d) 120601 = 09 (e) 120601 = 10 (f) 120601 = 11

(g) 120601 = 13 (h) 120601 = 15 (i) 120601 = 16



Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 08 (b) 120601 = 085 (c) 120601 = 09

(d) 120601 = 095 (e) 120601 = 10 (f) 120601 = 105

(g) 120601 = 11 (h) 120601 = 115 (i) 120601 = 12



Amp

1

A

0 x

Pha

0 x

(a) A = 08 (b)A = 09 (c) A = 10

120587


Amp

1

A

0 x

Pha

0 x

120587

(a) A = 08 (b)A = 09 (c) A = 10



Amp

1

0

w

x

Pha

0 x

120587

(d) w = 40mm (e) w = 50mm (f) w = 60mm










Examined lens

Detector


Pinhole d = 25mm

(a)

Yax

is (m

m)

X axis (mm)In

tens

ity (a

u)

110

3070 80 90 100 110 120 130 140 150

40

50

60

70

80

90

100

0

0002

0004

0006

0008

001

0012

0014

(b)









(a) (b) (c)



7 Conclusions





Competing Interests


Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






ℎmax = 120582119899 minus 1198990 (3)




119868119905 (119909) = 119868119894119890minus120572ℎ (4)


119879 = 119868119905 cos (120579119905)119868119894 cos (120579119894) (5)






119879 = 119860 (119909 119910) 119890119894120593(119909119910) (6)








135

14

145

15

155

Refr

activ

e ind

ex



03 05 07 09 11 13 1501Frequency (THz)

0

4

8

12

16

20

Abso

rptio

n co

effici

ent (

cmminus1)


135

145

155

165

175

Refr

activ

e ind

ex



03 05 07 09 11 13 1501Frequency (THz)

0

4

8

12

16

20

Abso

rptio

n co

effici

ent (

cmminus1)






(a) (b)












50mm

100mm


50mm

100mm


5 Simulations













Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 03 (b) 120601 = 05 (c) 120601 = 07

(d) 120601 = 09 (e) 120601 = 10 (f) 120601 = 11

(g) 120601 = 13 (h) 120601 = 15 (i) 120601 = 16



Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 08 (b) 120601 = 085 (c) 120601 = 09

(d) 120601 = 095 (e) 120601 = 10 (f) 120601 = 105

(g) 120601 = 11 (h) 120601 = 115 (i) 120601 = 12



Amp

1

A

0 x

Pha

0 x

(a) A = 08 (b)A = 09 (c) A = 10

120587


Amp

1

A

0 x

Pha

0 x

120587

(a) A = 08 (b)A = 09 (c) A = 10



Amp

1

0

w

x

Pha

0 x

120587

(d) w = 40mm (e) w = 50mm (f) w = 60mm










Examined lens

Detector


Pinhole d = 25mm

(a)

Yax

is (m

m)

X axis (mm)In

tens

ity (a

u)

110

3070 80 90 100 110 120 130 140 150

40

50

60

70

80

90

100

0

0002

0004

0006

0008

001

0012

0014

(b)









(a) (b) (c)



7 Conclusions





Competing Interests


Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








135

14

145

15

155

Refr

activ

e ind

ex



03 05 07 09 11 13 1501Frequency (THz)

0

4

8

12

16

20

Abso

rptio

n co

effici

ent (

cmminus1)


135

145

155

165

175

Refr

activ

e ind

ex



03 05 07 09 11 13 1501Frequency (THz)

0

4

8

12

16

20

Abso

rptio

n co

effici

ent (

cmminus1)






(a) (b)












50mm

100mm


50mm

100mm


5 Simulations













Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 03 (b) 120601 = 05 (c) 120601 = 07

(d) 120601 = 09 (e) 120601 = 10 (f) 120601 = 11

(g) 120601 = 13 (h) 120601 = 15 (i) 120601 = 16



Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 08 (b) 120601 = 085 (c) 120601 = 09

(d) 120601 = 095 (e) 120601 = 10 (f) 120601 = 105

(g) 120601 = 11 (h) 120601 = 115 (i) 120601 = 12



Amp

1

A

0 x

Pha

0 x

(a) A = 08 (b)A = 09 (c) A = 10

120587


Amp

1

A

0 x

Pha

0 x

120587

(a) A = 08 (b)A = 09 (c) A = 10



Amp

1

0

w

x

Pha

0 x

120587

(d) w = 40mm (e) w = 50mm (f) w = 60mm










Examined lens

Detector


Pinhole d = 25mm

(a)

Yax

is (m

m)

X axis (mm)In

tens

ity (a

u)

110

3070 80 90 100 110 120 130 140 150

40

50

60

70

80

90

100

0

0002

0004

0006

0008

001

0012

0014

(b)









(a) (b) (c)



7 Conclusions





Competing Interests


Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




(a) (b)












50mm

100mm


50mm

100mm


5 Simulations













Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 03 (b) 120601 = 05 (c) 120601 = 07

(d) 120601 = 09 (e) 120601 = 10 (f) 120601 = 11

(g) 120601 = 13 (h) 120601 = 15 (i) 120601 = 16



Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 08 (b) 120601 = 085 (c) 120601 = 09

(d) 120601 = 095 (e) 120601 = 10 (f) 120601 = 105

(g) 120601 = 11 (h) 120601 = 115 (i) 120601 = 12



Amp

1

A

0 x

Pha

0 x

(a) A = 08 (b)A = 09 (c) A = 10

120587


Amp

1

A

0 x

Pha

0 x

120587

(a) A = 08 (b)A = 09 (c) A = 10



Amp

1

0

w

x

Pha

0 x

120587

(d) w = 40mm (e) w = 50mm (f) w = 60mm










Examined lens

Detector


Pinhole d = 25mm

(a)

Yax

is (m

m)

X axis (mm)In

tens

ity (a

u)

110

3070 80 90 100 110 120 130 140 150

40

50

60

70

80

90

100

0

0002

0004

0006

0008

001

0012

0014

(b)









(a) (b) (c)



7 Conclusions





Competing Interests


Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




50mm

100mm


50mm

100mm


5 Simulations













Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 03 (b) 120601 = 05 (c) 120601 = 07

(d) 120601 = 09 (e) 120601 = 10 (f) 120601 = 11

(g) 120601 = 13 (h) 120601 = 15 (i) 120601 = 16



Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 08 (b) 120601 = 085 (c) 120601 = 09

(d) 120601 = 095 (e) 120601 = 10 (f) 120601 = 105

(g) 120601 = 11 (h) 120601 = 115 (i) 120601 = 12



Amp

1

A

0 x

Pha

0 x

(a) A = 08 (b)A = 09 (c) A = 10

120587


Amp

1

A

0 x

Pha

0 x

120587

(a) A = 08 (b)A = 09 (c) A = 10



Amp

1

0

w

x

Pha

0 x

120587

(d) w = 40mm (e) w = 50mm (f) w = 60mm










Examined lens

Detector


Pinhole d = 25mm

(a)

Yax

is (m

m)

X axis (mm)In

tens

ity (a

u)

110

3070 80 90 100 110 120 130 140 150

40

50

60

70

80

90

100

0

0002

0004

0006

0008

001

0012

0014

(b)









(a) (b) (c)



7 Conclusions





Competing Interests


Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 03 (b) 120601 = 05 (c) 120601 = 07

(d) 120601 = 09 (e) 120601 = 10 (f) 120601 = 11

(g) 120601 = 13 (h) 120601 = 15 (i) 120601 = 16



Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 08 (b) 120601 = 085 (c) 120601 = 09

(d) 120601 = 095 (e) 120601 = 10 (f) 120601 = 105

(g) 120601 = 11 (h) 120601 = 115 (i) 120601 = 12



Amp

1

A

0 x

Pha

0 x

(a) A = 08 (b)A = 09 (c) A = 10

120587


Amp

1

A

0 x

Pha

0 x

120587

(a) A = 08 (b)A = 09 (c) A = 10



Amp

1

0

w

x

Pha

0 x

120587

(d) w = 40mm (e) w = 50mm (f) w = 60mm










Examined lens

Detector


Pinhole d = 25mm

(a)

Yax

is (m

m)

X axis (mm)In

tens

ity (a

u)

110

3070 80 90 100 110 120 130 140 150

40

50

60

70

80

90

100

0

0002

0004

0006

0008

001

0012

0014

(b)









(a) (b) (c)



7 Conclusions





Competing Interests


Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Amp

1

0 x

Pha

0

120601

x

(a) 120601 = 08 (b) 120601 = 085 (c) 120601 = 09

(d) 120601 = 095 (e) 120601 = 10 (f) 120601 = 105

(g) 120601 = 11 (h) 120601 = 115 (i) 120601 = 12



Amp

1

A

0 x

Pha

0 x

(a) A = 08 (b)A = 09 (c) A = 10

120587


Amp

1

A

0 x

Pha

0 x

120587

(a) A = 08 (b)A = 09 (c) A = 10



Amp

1

0

w

x

Pha

0 x

120587

(d) w = 40mm (e) w = 50mm (f) w = 60mm










Examined lens

Detector


Pinhole d = 25mm

(a)

Yax

is (m

m)

X axis (mm)In

tens

ity (a

u)

110

3070 80 90 100 110 120 130 140 150

40

50

60

70

80

90

100

0

0002

0004

0006

0008

001

0012

0014

(b)









(a) (b) (c)



7 Conclusions





Competing Interests


Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Amp

1

A

0 x

Pha

0 x

(a) A = 08 (b)A = 09 (c) A = 10

120587


Amp

1

A

0 x

Pha

0 x

120587

(a) A = 08 (b)A = 09 (c) A = 10



Amp

1

0

w

x

Pha

0 x

120587

(d) w = 40mm (e) w = 50mm (f) w = 60mm










Examined lens

Detector


Pinhole d = 25mm

(a)

Yax

is (m

m)

X axis (mm)In

tens

ity (a

u)

110

3070 80 90 100 110 120 130 140 150

40

50

60

70

80

90

100

0

0002

0004

0006

0008

001

0012

0014

(b)









(a) (b) (c)



7 Conclusions





Competing Interests


Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Amp

1

0

w

x

Pha

0 x

120587

(d) w = 40mm (e) w = 50mm (f) w = 60mm










Examined lens

Detector


Pinhole d = 25mm

(a)

Yax

is (m

m)

X axis (mm)In

tens

ity (a

u)

110

3070 80 90 100 110 120 130 140 150

40

50

60

70

80

90

100

0

0002

0004

0006

0008

001

0012

0014

(b)









(a) (b) (c)



7 Conclusions





Competing Interests


Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Examined lens

Detector


Pinhole d = 25mm

(a)

Yax

is (m

m)

X axis (mm)In

tens

ity (a

u)

110

3070 80 90 100 110 120 130 140 150

40

50

60

70

80

90

100

0

0002

0004

0006

0008

001

0012

0014

(b)









(a) (b) (c)



7 Conclusions





Competing Interests


Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




(a) (b) (c)



7 Conclusions





Competing Interests


Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



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