Chemical composition, peroxide value and anisidine value of goat milk (GM), chromatographically purified algae oil (PAO), chromatographically purified Hibiscus mutabilis seed oil (PHMO), and natural Hibiscus mutabilis seed oil (NHMO).
\\n\\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\\n\\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'IntechOpen is proud to announce that 179 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\nThroughout the years, the list has named a total of 252 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\nReleased this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
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He has graduated from İstanbul Medical School, İstanbul University and become a medical doctor in 1989. Dr. Özdemir did his pediatric residency at Department of Pediatrics in Children’s Hospital, İstanbul Medical School, İstanbul, Turkey. His clinical fellowship training was finished at Pediatric Allergy/Immunology division in Louisiana State University, Health Sciences Centre, New Orleans, LA.\r\nDr. Ozdemir bench research areas are as follows: LAK-cell generation and cell-mediated cytotoxicity; human mast cell development and mast cell-mediated cytotoxicity; and apoptosis related research. \r\nHe was the first place winner of Clemens Von Pirquet Award from ACAAI at ACAAI meeting in 2005 for the best research on allergy/asthma/immunology by a fellow in training. \r\nDr. Ozdemir has more than 100 international plus 40 national publications, as well as 160 international and 140 national presentations, and more than 9 chapters related to my research areas. \r\nCurrently, he works as a chief of pediatrics associated with the division of pediatric allergy/immunology at Sakarya University, Medical School, Teaching and Training Hospital, Adapazarı, Sakarya, Turkey.",institutionString:"Sakarya 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"63279",title:"Phenolic Compounds in Hibiscus mutabilis Seeds and Their Effects on the Oxidative Stability of DHA-Enriched Goat Milk Emulsion",doi:"10.5772/intechopen.80541",slug:"phenolic-compounds-in-hibiscus-mutabilis-seeds-and-their-effects-on-the-oxidative-stability-of-dha-e",body:'Human breast milk contains both docosahexaenoic acid (DHA, C22:6n-3) and arachidonic acid (AA, C20:4n-6) [1], which are essential for health. Studies in animals and humans indicate that DHA is essential for normal visual and brain function in the premature infants and possibly in the full term infants [2, 3]. In some breast-fed infants, colic has been related to the mother’s consumption of cow milk [4, 5]. In older infants, the incidence of cow milk protein intolerance was encountered in 5–15% of cases [6]. A popular therapy among pediatricians is to change from cow milk to vegetable protein soy-based formula; however, infants with cow milk protein intolerance will also react adversely to soybean proteins [7]. When the problem is allergy to cow milk proteins (casein, whey), goat milk is a suitable substitute to cow milk [8].
The omega-3 fatty acids in the milk of grass-fed goats are predominantly linolenic acid (C18:3n-3), or alpha (α)-linolenic acid (ALA). DHA can be synthesized from dietary ALA, but the human body can only make very small amounts of DHA from ALA [9]. Therefore, there is a need to supplement foods with DHA. The addition of DHA from algae oil in food emulsions such as in goat milk emulsion requires the need for antioxidants. Antioxidants increase the shelf life of emulsions, but a clean label ingredient is required when added to milk. Oxidation in oil-in-water emulsions is thought to occur at the interface region between the oil and the aqueous phases [10]. In the oil phase of the emulsions, fatty acids are the target of free radicals i.e., hydroxyl radicals, which stimulate lipid peroxidation. Nonpolar antioxidants such as tocopherols and ascorbyl palmitate have been shown to be highly effective in protecting oil-in-water emulsions [11]. Tocopherols are free-radical terminators thereby, interrupting the free-radical chain of oxidative reactions by contributing hydrogen from the phenolic hydroxyl groups [12]. Ascorbyl palmitate, a lipid-soluble antioxidant, exhibits antioxidant activities that include single oxygen quenching and free-radical scavenging [13, 14, 15]. Ascorbyl palmitate has been shown to work synergistically with tocopherols by donating a hydrogen to the tocopheroxyl radical, formed as a result of tocopherol donating a hydrogen to the lipid radical [16, 17].
The oxidative stability of DHA-enriched emulsion may also be accomplished by the addition of vegetable oil to algae oil. In this context, one of the strategies developed to protect fish oil in a cow milk emulsion against oxidation was the mixing of rapeseed oil with fish oil prior to emulsification of cow milk [18]. The authors found that tocopherol isomers in concentrations similar to those found in natural rapeseed oil, and added to rapeseed oil stripped of natural tocopherols, significantly inhibited oxidation in cow milk emulsions enriched with fish oil [18].
Hibiscus mutabilis (Malvaceae) are shrubs with peach color flowers and originally native of China. The seeds of Hibiscus mutabilis, which do not have economic applications yet, are a source of vegetable oil. Although not widely reported in the literature, a high content of phenolic compounds, tocopherols are found in Hibiscus mutabilis seed oil. The seeds of Hibiscus mutabilis are also a source of lectin. Lectin from the seeds of Hibiscus mutabilis has carbohydrate-binding specificity to galactonic acid, which potently inhibited HIV-1 reverse transcriptase [19]. HIV, the RNA virus that causes AIDS, gradually disrupts the immune system in humans. Since a recent study suggested that DHA in high DHA-concentrated fish oil positively contributed to certain aspects of immune function in middle-aged obese adults [20], DHA-enriched goat milk stabilized by Hibiscus mutabilis seed oil potentially can be used as immune stimulator for the adjunctive therapy of HIV.
In the present work the suitability of Hibiscus mutabilis seed oil for enhancing the oxidative stability of DHA-enriched goat milk emulsion was studied. Based on the potential synergistic effects of ascorbyl palmitate with tocopherols, it was assumed that the most efficient oxidative stabilization during homogenization and storage of DHA-enriched goat milk may be achieved by combining both of these lipophilic antioxidants.
Raw milk from French-Alpine goats, raised at the International Goat Research Center, Prairie View A&M University, Prairie View, Texas, USA, was obtained. Raw milk with a fat content of 4.1% (wt/wt) that was determined according to the method of Kleyn et al. [21] was collected during the early lactation period. Iron and copper contents in raw goat milk were determined by atomic absorption spectrometry using a Varian SpectrAA 55 (Varian Analytical Instruments, Inc., Walnut Creek, CA, USA). Raw goat milk was dry-ashed in a muffle furnace (Barnstead/Thermolyne Corp., Dubuque, IA, USA) at 550°C. Ashes were dissolved in 0.2% nitric acid solution. The concentrations of iron and copper in raw goat milk were determined from the calibration curves that were produced under the same experimental conditions with known standards.
Algae oil was provided by Nutrinova Inc. (Somerset, NJ, USA). Algae oil was subjected to chromatography to remove peroxides, carotenoids, tocopherols, and other antioxidants, as previously described [22]. The chromatographically purified algae oil has a DHA concentration of 42.9% (Table 1). The fatty acid composition of chromatographically purified algae oil was determined by preparation of methyl esters [23], which were analyzed by gas chromatography–mass spectrometry (GC–MS). For the fatty acid profile of raw goat milk, the samples were centrifuged at 10,000× g for 1 h to harvest milk fat. Fatty acids of milk fat (% wt/wt) were directly methylated by in situ transesterification as described [24] and analyzed by GC-MS (Agilent model 7890A GC system attached to an Agilent model 5975C mass detector; Agilent Technologies Inc., Santa Clara, CA, USA) on a 30 m × 0.25 mm internal diameter, 0.25 μm film thickness capillary column. Methyl ester of 10, 13-nonadecadienoate (Nu-Chek-Prep U-58M, Elysian, MN, USA) was used as an internal standard. The concentrations of tocopherols in the raw goat milk and the chromatographically purified algae oil were determined by reversed-phase high-pressure liquid chromatography (HPLC) [25], and the results were expressed as μg/g of oil. The content of free fatty acids in the raw goat milk and the chromatographically purified algae oil was determined by AOAC method [26]. The fatty acid composition, the concentrations of tocopherols, the peroxide value (PV), the anisidine value (AV), and the content of free fatty acids in the raw goat milk and chromatographically purified algae oil samples are presented in Table 1.
Chemical composition, peroxide value and anisidine value of goat milk (GM), chromatographically purified algae oil (PAO), chromatographically purified Hibiscus mutabilis seed oil (PHMO), and natural Hibiscus mutabilis seed oil (NHMO).
The lipid-soluble antioxidant, ascorbyl palmitate, was purchased from DSM Nutritional Products, Inc. (Parsippany, NJ, USA). All reagents used were of analytical grade, ACS certified or HPLC grade, from Sigma-Aldrich (St. Louis, MS, USA). Deionized water was prepared by passing distilled water over a mixed bed of cation-anion exchanger and was used throughout this study.
Fresh harvested seeds of Hibiscus mutabilis (Figure 1) were obtained from The Village Botanica, Inc. (Waller, TX, USA). The seeds were immediately frozen with liquid nitrogen until analysis. The frozen seeds were thawed, dried by air blower and then milled using a blender. The ground samples that passed through a 35-mesh sieve were used for oil extraction.
Image of seeds of Hibiscus mutabilis.
The ground fractions of Hibiscus mutabilis seeds were placed in a filter paper (Whatman No. 42) and introduced in a cartridge and they were extracted in a Soxhlet extractor (Southern Labware, Inc., Cumming, GA, USA) using hexane at 65–70°C during approximately 5 h, the time necessary to extract most of the oil from the seeds. The solvent was then evaporated by a vacuum dryer (Columbia International Tech, Irmo, SC, USA), and the oil yield was 9.0 g from 100 g of seeds. The extracted Hibiscus mutabilis seed oil was transferred into glass tubes, centrifuged at 12,000× g for 30 min at room temperature, and then stored at 4°C in the dark until analyses. This oil is referred to as the natural Hibiscus mutabilis seed oil (Table 1). The natural Hibiscus mutabilis seed oil was subjected to chromatography to remove naturally occurring antioxidants such as tocopherols and carotenoids [22]. Thus, this Hibiscus mutabilis seed oil is void of antioxidants and peroxides. The percent fatty acid composition of the chromatographically purified Hibiscus mutabilis seed oil and the natural Hibiscus mutabilis seed oil were determined according to procedures described [23] by GC–MS. The fatty acid composition of the chromatographically purified Hibiscus mutabilis seed oil was similar to the natural Hibiscus mutabilis seed oil (Table 1). The content of free fatty acids in the chromatographically purified Hibiscus mutabilis seed oil and the natural Hibiscus mutabilis seed oil was determined by AOAC method [26]. The concentrations of tocopherols, the PV, the AV, and the concentrations of free fatty acids of the natural and the chromatographically purified Hibiscus mutabilis seed oil samples are presented in Table 1.
Three liters of raw goat milk was pasteurized by heating at 72°C and holding milk at this temperature for 15 s. Chromatographically purified algae oil (0.25 wt%), chromatographically purified Hibiscus mutabilis seed oil (0.25 wt%) or natural Hibiscus mutabilis seed oil (0.25 wt%) with and without ascorbyl palmitate (200 μg/g of oil) were added to goat milk. Goat milk samples were then cooled to 50°C and immediately homogenized at 22.5 MPa (3263.35 psi) through a high-pressure TC5 homogenizer (Stansted Fluid Power, Harlow, UK). The goat milk emulsion samples were transferred to sterile 100-ml Pyrex dark brown glass bottles, which were flushed with nitrogen and then stored at 2°C in the dark for 14 days. The goat milk emulsions, with added oils, were labeled as follows: PAO = chromatographically purified algae oil, PHMO = chromatographically purified Hibiscus mutabilis seed oil, NHMO = natural Hibiscus mutabilis seed oil, and LAAP = lipid-soluble antioxidant ascorbyl palmitate.
The particle size of the oil droplets in the goat milk emulsions was measured at day 1 and day 14 at 21 ± 1°C with a SALD-2101 laser diffraction particle size analyzer (Shimadzu Corporation, Columbia, MD, USA). The emulsion samples were diluted 100 times with double deionized water before they were transferred into the chamber of the instrument. Particle size measurements in μm were carried out in triplicate.
Lipids from the DHA-enriched goat milk emulsions were extracted by chloroform:methanol (1:1 wt/wt), using a small volume of solvent [27, 28]. The PV was measured directly on the oils or fats extracted from the DHA-enriched goat milk emulsions by colorimetric determination of iron thiocyanate [29]. This method measures primary oxidation products of oils or fats i.e., hydroperoxides of oils and fats. The mean measurements in meq/kg of three replicates were reported.
The para (p)-anisidine value was determined in the DHA-enriched goat milk emulsions by AOAC method [30]. This method determines the amount of aldehydes (principally 2-alkenals and 2,4-dienals) present in the emulsion samples. The mean measurements of three replicates were reported.
The results of triplicate analyses were expressed as means ± standard deviations. The data were analyzed by ANOVA using PRO GLM procedure of SAS (version 8.2, SAS Institute, Cary, NC, USA). The least significant difference test was used to determine significant differences among treatment means at p < 0.05.
The rate and extent of oxidation of marine oils i.e., algae oil, fish oil depends on the matrix of the food to be fortified. Milk relative to some other foods offers good protection against oxidation, since these marine oils are emulsified and stabilized by the casein micellar structure [18]. Casein adsorbs to the newly formed interface thereby, providing enhanced protection by forming a physical barrier [31, 32]. Although milk is stored in refrigerators (2–4°C) and has a relatively short life (21 days), it is still subject to overall stress due to UV and visible light, temperature fluctuations, and handling abuse.
Lipid oxidation proceeds from the interface to the oil droplet interior in oil-in-water emulsions i.e., goat milk emulsion, therefore, the susceptibility of lipids to oxidation at the interface is the most important factor affecting the oxidative stability of lipids in food and beverage emulsions. It is generally accepted that the attack of free radicals and trace metals on lipids at the interface increases with the increase in the area of interface. Thus, the oxidative stability of DHA in goat milk emulsions should decrease with decreasing droplet sizes. The results of the droplet size determinations (Table 2) showed that the droplets did not change in size from day 1 to day 14 of storage at 2°C, indicating that the goat milk emulsions were physically stable during the 2 weeks of storage. The average droplet size in all goat milk emulsions containing 0.5% oil was from 1.20 ± 0.01 to 1.25 ± 0.03 μm, while the droplet size in the original goat milk sample was 0.89 ± 0.02 μm. These results showed that the sizes of droplets in goat milk emulsions containing 0.5% added oil, irrespective of the oil type, were significantly (p < 0.05) larger than the droplets in the original goat milk sample. The decrease in the oil droplet size induces the increase in the droplet interface [33], from which the oxidation proceeds to the oil droplet interior. The results of Table 2 suggest that DHA in goat milk emulsions containing 0.5% added oil is expected to be less oxidized in the droplet interior.
Droplet sizes of goat milk emulsions prepared by mixing chromatographically purified algae oil (0.25 wt%), chromatographically purified Hibiscus mutabilis seed oil (0.25 wt%) or natural Hibiscus mutabilis seed oil (0.25 wt%) with and without added ascorbyl palmitate (200 μg/g of oil) during 14-day storage at 2°C.
When supplementing foods with algae oil or fish oil, it is important to consider the initial quality of the raw material. In this work, we have ensured that all oils tested had similar variables such as age and storage temperature. The results of Table 1 showed that all oils had low initial values of PV, and very low content of free fatty acids. Rancid flavors in goat milk is usually associated to the release of short-chain free fatty acids and is a persistent problem in dairy goat farms due to mishandling procedures starting from the farm until it reaches the consumers. The content of free fatty acids in the goat milk used in this study was very low (0.1%) and likewise, the PV content of goat milk was also low (0.1 meq/kg) suggesting that the quality of goat milk was acceptable from the sensory perspectives.
As to the goat milk emulsions, the chromatographically purified Hibiscus mutabilis seed oil (PHMO) together with the chromatographically purified algae oil (PAO) had a significantly (p < 0.05) higher PV than the other two goat milk emulsions at each storage time at 2°C (Figure 2). On the other hand, the goat milk emulsion with the natural Hibiscus mutabilis seed oil (NHMO) and the chromatographically purified algae oil (PAO) exhibited good oxidative stability as inferred from a low PV (Figure 2). The goat milk emulsion containing the chromatographically purified algae oil (PAO) and the natural Hibiscus mutabilis seed oil (NHMO) with added ascorbyl palmitate (LAAP) had the lowest PV during the study (Figure 2). These results suggest that the presence of antioxidants i.e., γ-tocopherol, ascorbyl palmitate improved the oxidative stability of goat milk emulsions under storage at 2°C for 14 days, which may contribute to the shelf life of goat milk emulsions.
Peroxide values of goat milk emulsions containing the different oils with and without added ascorbyl palmitate during 14-day storage at 2°C. Means (n = 3) within each storage day with different letters (a–c) are significantly different (p < 0.05).
The key challenge in formulating food products with marine oils is their sensitivity to iron and copper, catalysts to oxidation that exists in even the cleanest water, foods, and other ingredients. The goat milk used in this study, contained approximately 138 ppb iron and 27 ppb copper, and these values were not affected by the addition of oils to the goat milk. The presence of trace metals in goat milk is expected to accelerate the degradation of lipid hydroperoxides as well as the degradation of the secondary oxidation products into shorter chain volatiles.
The results of Figure 3 showed that the goat milk emulsions containing a mixture (1:1) of the chromatographically purified algae oil (PAO) and the chromatographically purified Hibiscus mutabilis seed oil (PHMO) were more oxidized than the goat milk emulsions containing a mixture (1:1) of the chromatographically purified algae oil (PAO) and the natural Hibiscus mutabilis seed oil (NHMO). The protective effect of the natural Hibiscus mutabilis seed oil (NHMO) may be partially ascribed to the high content of tocopherols, especially γ-tocopherol. As pointed out earlier, the tocopherols are free-radical terminators, which donate a hydrogen to the peroxyl radical [12]. Goat milk contains citric acid [34], and citric acid is recognized as a metal chelator. The chelating properties of citric acid have been proposed to protect tocopherols during oxidation [35]. Therefore, citric acid in goat milk could enhance the antioxidant activity of tocopherols in the emulsions containing the natural Hibiscus mutabilis seed oil (NHMO) and the chromatographically purified algae oil (PAO) at 1:1 ratio (Figure 3).
p-Anisidine values of goat milk emulsions containing the different oils with and without added ascorbyl palmitate during 14-day storage at 2°C. Means (n = 3) within each storage day with different letters (a–c) are significantly different (p < 0.05).
Ascorbyl palmitate (LAAP), which was added (200 μg/g of oil) to the natural Hibiscus mutabilis seed oil (NHMO) and the chromatographically purified algae oil (PAO) at 1:1 ratio, significantly reduced (p < 0.05) the extent of oxidation in this goat milk emulsion at 7-day and 14-day storage at 2°C (Figure 3). This protective effect of added ascorbyl palmitate (LAAP) was not observed in goat milk emulsions containing the chromatographically purified Hibiscus mutabilis seed oil (PHMO) and the chromatographically purified algae oil (PAO) at 1:1 ratio during 14-day storage at 2°C (data not shown). Ascorbyl palmitate (LAAP) had a more pronounced protective effect on the goat milk emulsion prepared with the chromatographically purified algae oil (PAO) and the natural Hibiscus mutabilis seed oil (NHMO) at 1:1 ratio by working synergistically with the γ-tocopherol isomer at 7-day and 14-day storage at 2°C (Figure 3). It is likely that ascorbyl palmitate retarded oxidation during storage of oil-in-water emulsions by direct scavenging of free radicals and tocopherol regeneration [18].
There is a direct relationship between the level of oxidation and sensory deterioration and even at times when there are no detectable oxidation parameters, the taste of the finished products could be displeasing. The decomposition of lipid hydroperoxides from marine derived n-3 polyunsaturated fatty acids (PUFAs), such as docosahexaenoic acid (DHA, C22:6n-3) and eicosapentaenoic acid (EPA, C20:5n-3), produces undesirable rancid and fishy off-flavors. Future work will evaluate the sensory attributes of DHA-enriched goat milk emulsion stabilized by the natural Hibiscus mutabilis seed oil and ascorbyl palmitate.
This work showed the suitability of using Hibiscus mutabilis seed oil to protect marine-derived n-3 PUFAs in oil-in-water emulsions i.e., DHA-milk from oxidative degradation for 14 days at 2°C. The natural Hibiscus mutabilis seed oil efficiently protected the chromatographically purified algae oil from oxidation during emulsification and storage of DHA-enriched goat milk emulsion. The addition of ascorbyl palmitate to the natural Hibiscus mutabilis seed oil and the chromatographically purified algae oil prior to goat milk emulsification had a significant (p < 0.05) protective effect on DHA-enriched goat milk emulsion. The combination of differences in fatty acid composition and concentration of tocopherols for the natural Hibiscus mutabilis seed oil seems to affect the oxidative stability of the goat milk emulsions prepared with this oil. This study provides a useful precedent for understanding the antioxidant activity of Hibiscus seed oils in food and beverage emulsions containing marine n-3 PUFAs.
Complementary work is currently being performed in our laboratory to optimize the oxidative stability of DHA-enriched goat milk emulsions with added seed oils from Hibiscus species such as Hibiscus moscheutos and Hibiscus dasycalyx to be able to withstand the thermal and mechanical stresses of industrial processes.
This work was supported by Evans-Allen funding to the Cooperative Agricultural Research Center through USDA Cooperative State Research Service.
The authors declare that they have no conflict of interest.
Holography is the only visualization technique that satisfies all the depth cues [1, 2, 3]. Therefore, it gives a natural three-dimensional (3D) visualization. Holography is based on capturing the diffracted optical waves from an object and regenerating those waves again by illuminating the recording media [1, 2, 3, 4, 5, 6]. Captured optical waves provide a significant amount of information related to the object such as surface profile, depth, and refractive index of the object. Hence, holography has a myriad of applications. For instance, holograms can be used as optical elements like prisms, lenses, and mirrors [7, 8]. Also, parallel optical computing is possible when holograms are employed [9, 10]. Furthermore, holograms are useful in metrology [11, 12, 13] and microscopic imaging to visualize very small objects like cells and bacterias [14, 15]. Another application of holography is related to nondestructive testing [16, 17, 18]. Nevertheless, major application of holography is related to 3D visualization, and it is used in education [19, 20], dentistry [21, 22], gaming [23], demonstration of cultural heritage [24], and more.
\nHolography setups can be assembled by using different configurations depending on the application. In optical holography setups, holographic patterns are stored on high-resolution holographic films [25, 26] and some type of crystals [27]. However, in some of the applications, we need to process the captured holographic patterns by numerical methods. Then, digital sensing devices are employed as a capturing device. Those types of setups are called as digital holography, and it has a vast amount of applications especially in nondestructive testing and microscopy. In [28], digital holography-based measurement method of 3D displacement is presented. Observed material is illuminated from four different directions sequentially; then they are combined to improve the resolution in the order of 10 nm. As a nondestructive testing method, digital holography is used in the analysis of cortical bone quality and strength impact in [29]. Furthermore, a method based on digital holography is implemented for detecting and measuring effect of moisture on the hygroscopic shrinkage strain on wood [30]. Another application of digital holography is in precise and accurate measurement of the initial displacement of the canine and molar in human maxilla [31]. By using subpixel registration and fusion algorithms, an improvement of profile measurements and expanding the field of view (FOV) in continuous-wave terahertz reflective digital holography is achieved [32]. A comprehensive review of denoising methods on phase retrieval from digital holograms in terms of signal-to-noise ratio (SNR) and computation time is presented in [33]. Removal of phase distortions by using principal component analysis (PCA) method is given in [34].
\nHolography is a versatile tool for visualization, measurement, and testing. In optical and digital holography methods, we need some optical sensing elements like polymers and digital devices to capture the diffracted field from the object. However, in computer-generated holography (CGH), diffraction field calculations are performed by using numerical methods and signal processing algorithms [4, 5, 6, 35]. Then, we can obtain the hologram from the calculated diffraction field and use it to drive dynamic display devices such as spatial light modulators (SLMs). After that, illumination of the SLM with a coherent light source will provide an optical reconstruction of the original object. When CGHs are calculated sequentially and used in driving SLMs, then we can have a holographic 3D television (H3DTV) as a product. An overview on holographic displays is presented in [36]. Generally, coherent light sources are used in H3DTV systems, and those light sources can generate speckle noise in the reconstructions. Low computational method for improving image quality and decreasing the speckle noise in CGH is proposed in [37]. Diffraction field calculations as in CGH are also used in other 3D display systems to improve the resolution of reconstructed objects. For instance, in integral imaging-based 3D display system, distortions on the elemental images are corrected by using holographic functional screen [38].
\nIn diffraction field calculation from a 3D object, we have to generate a synthetic 3D object. There are plenty of ways for generating a synthetic 3D object in a computer. For instance, we can form a 3D object by using a set of point light sources which are distributed over the space. Those types of objects are called as point cloud objects. To calculate the diffraction field from a point cloud object, we superpose the diffraction fields emitted by each point light source [35, 39, 40, 41, 42, 43, 44]. Another 3D object generation method is based on stitching small planar patches. As in the process of diffraction field calculation from point cloud objects, once again the diffracted fields from each patch are superposed to obtain the diffraction field of the object [45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55]. The third method which can be used in the generation of synthetic 3D object is based on having multiple two-dimensional (2D) cross sections of the object along the longitudinal axis. Then, superposition of diffracted fields from those 2D cross sections will give the diffraction field of the 3D object [56, 57, 58, 59, 60]. A detailed summary on CGHs in terms of resolution, field of view, eye relief, and optical setups for different 3D object generation methods can be seen in [61, 62].
\nCGHs of the objects should be calculated rapidly to obtain H3DTV systems. Hence, fast methods such as fast Fourier transform (FFT) and look-up table (LUT)-based methods are utilized in CGH calculations. In [39, 52], algorithms which are based on FFT are used for decreasing the calculation time of CGH. Precomputed LUTs are also used for achieving fast calculations in CGH calculations [2, 39, 41, 42, 63, 64]. Another way to achieve fast calculation in CGH is based on segmentation of diffraction field from point light sources [43, 44]. Parallel processing of diffraction field calculation provides further improvements on the computation time. Graphical processing units (GPUs) are special hardware to run parallel calculations. Thus, they are one of the most convenient hardware for H3DTV systems [40, 44, 65, 66]. Time-division method can also be used in the calculation of CGHs for layered 3D objects to achieve fast computations [67].
\nImposing some approximations in the diffraction field calculations provides to decrease the computational complexity, and it paves the way to obtain fast diffraction field calculations. In the meantime, we have to improve the quality of the reconstructed object. An accurate calculation method of diffraction field which is based on angular spectrum decomposition is explained in [68]. Furthermore, diffraction field calculation methods for SLMs with pixelated structure are presented in [69, 70, 71]. However, the computational complexities of those methods are too high to have real-time diffraction field calculations. As a result of this, the algorithms presented in [72, 73, 74, 75] are proposed as a solution to both computation time and quality in the reconstructed object in H3DTV. Further computational time improvements can be obtained by utilizing a LUT which is optimized for parallel processing on a GPU to achieve real-time calculations. Moreover, the pixel structure of the employed SLM in the reconstruction process is taken into account in forming LUT. Calculated LUT has one-dimensional (1D) kernels to decrease the allocated memory space.
\nIn CGH, it is possible to obtain 3D reconstructions of both synthetic and real objects. By employing dynamic display devices like SLMs in the reconstruction process, we can have H3DTV systems. To drive SLMs, we have to calculate diffraction fields from 3D objects by using numerical analysis methods and signal processing techniques. Calculation of diffraction field depends on the 3D object generation method. In this work, we assumed that 3D objects are represented as point clouds, because it is one of the simplest methods in 3D object generation. The diffraction field of the 3D object is calculated by superposing the diffraction fields emitted from the points that form the 3D object.
\nSuperposition on diffraction field calculation from a point cloud object over a planar surface can be expressed as
\nwhere \n
\n\n
where \n
Scaled and superposed diffraction fields from point light sources provide the diffraction field of the 3D object, and its phase component is used for driving the SLM. Then, entire surface of the SLM is illuminated by a plane wave. After that, the reflected optical wave from the surface of the SLM generates an optical replica of the 3D object. Most of the off-the-shelf SLMs have square pixels with very high filling factors like \n
An illustration of the pixel structure of the simulated SLM.
Simulation of optical setup can be improved when the pixelated structure of the SLM is taken into consideration. For that purpose, we have to perform surface integration over each pixel area on the SLM. It is assumed that gray value over each pixel area has a constant value. The diffraction field over SLM can be found as
\nwhere \n
where \n
where \n
and its elements can be calculated as
\nwhere \n
Numerical evaluation of cosine and sine Fresnel integrals given in Eq. (8) is calculated by adaptive Lobatto quadrature [77].
\nIn the standard algorithm, diffraction field of each point is obtained by evaluating Eq. (8). Then, superposition of those fields is performed to obtain CGH. As a result of this, computational complexity of diffraction field calculation is too high to have real-time applications. As a solution to the computation time problem, we present a fast algorithm to calculate 2D kernel, \n
Fast computation of diffraction field and improved quality of reconstructed 3D object are essential issues in H3DTV. As a solution to those problems, we propose a method based on calculation of 2D kernels \n
where \n
Performance assessment of the proposed diffraction field calculation method is obtained by implementing different scenarios, but a few of them are presented to give an insight to the reader. Two major performance evaluation criteria are taken into account: total computation time of the CGH and the normalized mean square error (NMSE) on the reconstructed object. NMSE on the reconstructed object can be calculated as
\nwhere \n
An illustration of simulated optical setup. The SLM employed in the setup has \n\nN\n\n and \n\nM\n\n pixels along \n\nx\n\n- and \n\ny\n\n-axes, respectively. Transversal axis sampling is indicated by \n\n\nX\ns\n\n\n. The variable \n\n\nz\n0\n\n\n determines the distance between SLM and the closest point light source of the 3D object.
First, a 3D point cloud object is generated in computer environment. The generated 3D object has \n
The proposed algorithm is implemented by using two platforms: MATLAB and Visual C++. To have shorter computation time for diffraction fields, we utilize CUDA libraries and parallel computation power of GPU. The assembled computer system has i5-2500 CPU at 3.3 GHz, 4GB RAM, and a GTX-680 GPU to run the algorithm. Operating system of the computer is chosen as 64-bit Windows 7.
\nGenerally, off-the-shelf SLMs have pixelated structure, and phase parts of the calculated diffraction fields are used for driving the SLM. When the pixelated structure of SLM is not taken into account in CGH calculations, it is not easy to differentiate focused and unfocused parts of the reconstructed 3D objects. An illustration of such a result can be seen in Figure 3a. As a result of the similarity in focused and unfocused parts, the quality of the reconstructed object is decreased significantly. On the contrary, the difference between focused and unfocused parts in the reconstructed 3D object is clear when the proposed method is used in diffraction field calculation. Those results can be seen easily in Figure 3b.
\nA point cloud object which has six parts and each part is located at different depths along the longitudinal axis. The leftmost piece is reconstructed in both of the figures shown above: (a) reconstruction of the 3D object from the CGH obtained without taking into consideration the pixelated structure of SLM and (b) reconstruction from the CGH calculated by the proposed algorithm.
Furthermore, numerical and optical reconstructions are very similar to each other, and that similarity in the reconstructions can be seen in Figure 4.
\n(a) Optical reconstruction of a point cloud object and (b) numerical reconstruction of the same object given in (a).
To calculate the diffraction field in the standard method, we need to perform cosine and sine Fresnel integrals for each pixel on SLM and for each point light source in 3D object. As a result of this, computational complexity of the standard method is extremely high, and CGH is calculated at \n
3D object = 3144 points; \n | \nComputation time (s) | \nNMSE | \n
---|---|---|
Standard method | \n2710.10 | \n— | \n
LUT | \n8.15 | \n0.08 | \n
LUT: parallel processing by using four cores | \n7.08 | \n0.08 | \n
LUT: parallel processing by using GTX-680 | \n0.08 | \n0.08 | \n
Performance assessment of the proposed algorithm in terms of NMSE.
Proposed algorithm utilizes LUT which has 1D precomputed kernels for 125 different sampling points along longitudinal axis.
By increasing the number of kernels in LUT, we can improve error performance of the algorithm without having any extra computational load, but there is an increase in the size of the required memory. As a result of this, installed memory space may not be enough to perform the diffraction field calculations. To overcome memory allocation problem, we use another sampling policy in generation of LUT. Two different sampling policies along the longitudinal axis are proposed. The first sampling policy is based on uniform sampling of longitudinal axis. The second sampling policy is related to uniform sampling of \n
3D object = 3144 points; \n | \n||
---|---|---|
Number of 1D kernels | \nNMSE | \nMemory allocation (kB) | \n
83 | \n0.068 | \n332 | \n
92 | \n0.061 | \n368 | \n
103 | \n0.054 | \n412 | \n
118 | \n0.048 | \n472 | \n
137 | \n0.039 | \n548 | \n
165 | \n0.034 | \n660 | \n
206 | \n0.026 | \n824 | \n
274 | \n0.020 | \n1096 | \n
411 | \n0.014 | \n1644 | \n
821 | \n0.006 | \n3284 | \n
Performance of the proposed algorithm according to the number of kernels used in LUT, NMSE, and allocated memory space.
LUT is formed by uniform sampling of depth parameter along longitudinal axis. Each element in 1D kernels is represented by four bytes.
3D object = 3144 points; \n | \n||
---|---|---|
Number of 1D kernels | \nNMSE | \nMemory allocation (kB) | \n
83 | \n0.127 | \n332 | \n
92 | \n0.114 | \n368 | \n
103 | \n0.104 | \n412 | \n
118 | \n0.088 | \n472 | \n
137 | \n0.077 | \n548 | \n
165 | \n0.062 | \n660 | \n
206 | \n0.051 | \n824 | \n
274 | \n0.038 | \n1096 | \n
411 | \n0.025 | \n1644 | \n
821 | \n0.013 | \n3284 | \n
Performance of the proposed algorithm according to the number of kernels used in LUT, NMSE, and allocated memory space.
LUT is formed by uniform sampling of \n
In terms of calculated numerical errors, there should be a significant amount of deviation between reconstructed objects from CGHs obtained by standard and proposed method, but it is not easy to differentiate the reconstructions visually. Illustrations of numerically reconstructed objects by using both methods are shown in Figure 5a and b, respectively. To see the difference between to reconstructions, we subtract two reconstructions from each other and then take the magnitude of that difference. Then, we scale difference image linearly between 0 and 255 to improve the visibility of insignificant deviations. Those deviations can be seen in Figure 5c. Most of the deviations are in the unfocused region, and those deviations will not decrease the quality of the reconstruction. As a result of this, the proposed algorithm provides successful results.
\n(a) Magnitude of the reconstructed object at \n\nz\n=\n\nz\n0\n\n\n from the diffraction pattern calculated by standard algorithm and (b) by the proposed algorithm. (c) Magnitude of the difference between the reconstructed objects given in (a) and (b). Please note that image is scaled linearly from 0 to 255; thus the insignificant differences may become visible.
Performance assessment of the presented algorithm is tested by optical reconstructions as well. For that purpose, we assembled an optical setup which is shown in Figure 6. Green laser with \n
Assembled optical setup for optical experiments.
Optically reconstructed 3D objects: (a) hand (b) propeller.
Two major problems in H3DTV systems can be called as decreasing the computation time of CGH and improving the quality of the reconstructed object. Using fast algorithms in diffraction field calculations will be helpful to decrease the computation time, but most of those fast algorithms impose some approximations that decrease the quality of the reconstructed object. In this work, we propose a diffraction field calculation algorithm that paves the way to achieve real-time calculations of diffraction fields from point cloud objects. In the meantime, the quality of the reconstructed objects is improved by taking into account the pixelated structure of SLM. Also, the proposed method can be run in parallel on a GPU. Performed numerical and optical experiments provide similar results. The proposed method utilizes precomputed LUT to decrease the computational load. To store the precomputed LUT, we need significant amount of memory allocation, and optimization of the occupied memory space is obtained by having two different sampling policies along the longitudinal axis. In the first sampling policy, LUT is formed by having uniform sampling along longitudinal axis. In the second one, nonuniform sampling is applied. When we fix size of the LUT, better NMSE performance is obtained by uniform sampling policy. As a result of this, when we use uniform sampling policy in computation of LUT, we need to allocate less amount of memory to store it.
\nThis work was supported by the Scientific and Technological Research Council of Turkey project under grant EEEAG-112E220 and Marmara University Scientific Research Fund project under grant FEN-A-130515-0176.
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