Statistical interferometry based on the statistics of speckle phase

Label-free optical interferometric microscopy to characterize morphodynamics in living plants

During the last century, fluorescence microscopy has played a pivotal role in a range of scientific discoveries. The success of fluorescence microscopy has prevailed despite several shortcomings like measurement time, photobleaching, temporal resolution, and specific sample preparation. To bypass these obstacles, label-free interferometric methods have been developed. Interferometry exploits the full wavefront information of laser light after interaction with biological material to yield interference patterns that contain information about structure and activity. Here, we review recent studies in interferometric imaging of plant cells and tissues, using techniques such as biospeckle imaging, optical coherence tomography, and digital holography. These methods enable quantification of cell morphology and dynamic intracellular measurements over extended periods of time. Recent investigations have showcased the potential of interferometric techniques for precise identification of seed viability and germination, plant diseases, plant growth and cell texture, intracellular activity and cytoplasmic transport. We envision that further developments of these label-free approaches, will allow for high-resolution, dynamic imaging of plants and their organelles, ranging in scales from sub-cellular to tissue and from milliseconds to hours.

A method for continuously monitoring the quality of Masson pine seedlings

Root growth potential (RGP) is a popular physiological indicator used to evaluate seedling vigor. However, the time scale used in the RGP test is the order of days, which leads to poor performance of the RGP method. We propose an optical interference method, called statistical interferometry, to measure minute root elongation at a sub-nanometer scale, which can decrease the time used in measuring RGP. The time scale of this method is also 10⁴ times less than that of the RGP method. Because we can measure the length of root elongation continuously, we can compute the root elongation rate (RER), which is the variety of the length of root elongation per second. Continuous monitoring can help determine the quality of Masson pine seedling as soon as possible. To show the effectiveness of our proposed method, we designed an experiment, in which we applied different water stresses to our collected Masson pine seedlings and acquired two groups of pines, representing two different qualities: one stressed by water and one not. After measuring the RER of the groups in our experiments, we found that RER is interrelated with the quality of seedlings.

Nanometer accuracy statistical interferometric technique in monitoring the short-term effects of exogenous plant hormones, auxin and gibberellic acid, on rice plants

Statistical interferometric technique (SIT) is a highly sensitive, high speed non-contact, and non-destructive optical technique developed by our group capable of measuring instantaeoues sub-nanometer displacements. SIT applied to plant leaf elongation revealed nanometric intrinsic fluctuaitons (NIF) that are robust and sensitive to variations in the environment making NIF as a measure of healthiness of the plants. In this study, exogenous plant hormones, auxin (2,4-dichlorophenoxyacetic acid-2,4-D), and gibberellic acid (GA₃), along with an auxin transport inhibitor 2,3,5-triiodobenzoic acid-TIBA, that affect plant growth were used to investigate their effects on NIF. Rice (Oriza sativa) seedlings were used, and their roots were exposed to 1, 2, and 4 µM 2,4-D, and the auxin transport inhibitor, TIBA, of 10, and 20 µM for 22 h and GA₃ solution of different concentrations of 10, 40, and 100 µM for 5 h. Results showed significant increment in NIF for 1 µM and reduction for 4 µM 2,4-D while applicaiton of both 10, and 20 µM TIBA led to reduction in NIF. On the other hand, significant increment in NIF for 40 µM, and a significant reduction at a higher concentration of 100 µM for 5 hours of GA₃ were also observed in comparison to those of control. Our results indicate that NIF as revealed by SIT could show both the positive and negative effects depending on the concentration of exogenous hormones, and transport inhibitors. Results suggest that SIT could be a valuable tool being sensitive enough to speedily assess the effects of plant growth hormones.

Object wave retrieval using normalized holograms in three-step generalized phase-shifting digital holography

Phase-shifting methods using interferogram normalization are often applied to smooth objects, for which the requirements for the normalization approach, including zero-order term elimination and the norm approximation condition, are easily achieved. Here we propose a three-step generalized phase-shifting method using the normalization approach for diffuse objects. In the proposed method, the zero-order terms are sufficiently suppressed by mutual subtraction of the phase-shifted holograms. The norm approximation condition is satisfied, and the complex field of the object wave can be estimated by the normalization approach when the hologram satisfies the phase randomness condition. We present an object wave retrieval algorithm using three phase-shifted holograms, in which estimation of phase-shift values is unnecessary. The proposed method is verified through simulations and optical experiments.

Highly sensitive optical interferometric technique reveals stress-dependent instantaneous nanometric growth fluctuations of Chinese chive leaf under heavy metal stress

Plant growth apart from being a complex and highly dynamic is dependent on its immediate environment. Leaf expansion measurements using Statistical Interferometry Technique, a sensitive interferometric technique at nanometric accuracy and at sub-second levels revealed the presence of characteristic nanometric intrinsic fluctuations [Plant Biotechnology 31, 195 (2014)]. In this paper, we demonstrate that the nanometric intrinsic fluctuations are sensitive enough that they change under exposure of heavy metals, essential micronutrient zinc and non-essential element cadmium, at relatively low concentrations in the leaves of Chinese chive (Allium tuberosum). The nanometric intrinsic fluctuations of leaves were observed for 4h under three cadmium concentrations or two zinc concentrations. Results showed significant reduction of nanometric intrinsic fluctuations for all cadmium concentrations, and in contrast significant increase of nanometric intrinsic fluctuations for all zinc concentrations. There was significant reduction of nanometric intrinsic fluctuations for cadmium exposure of concentrations of 0.001mM for even an hour, and significant increment of nanometric intrinsic fluctuations under 0.75mM zinc from 1hr exposure. For comparison, antioxidative enzymes and metal uptake were also measured under 4hr exposure of cadmium or zinc. However, no significant changes could be seen in antioxidative enzymes within 4h under the smaller concentration of 0.001mM cadmium as seen for nanometric intrinsic fluctuations. The results imply that nanometric intrinsic fluctuations can be not only used as a measure for heavy metal stress but also it can be more sensitive to detect the toxic as well as positive effects of smaller amounts of heavy metal on plants at an early stage.

Phase retrieval by Euclidean distance in self-calibrating generalized phase-shifting interferometry of three steps

This paper presents a novel algorithm for phase extraction based on the computation of the Euclidean distance from a point to an ellipse. The idea consists in extracting the intensities from a data row or column in three interferograms to form points of intensity and then fitting them to an ellipse by the method of least squares. The Euclidean distance for each intensity point is computed to find a parametric phase whose value is associated to the object phase. The main advantage of the present method is to avoid the use of tangent function, reducing the error in the desired phase computation.

Nanometer-scale elongation rate fluctuations in the Myriophyllum aquaticum (Parrot feather) stem were altered by radio-frequency electromagnetic radiation

The emission of radio-frequency electromagnetic radiation (EMR) by various wireless communication base stations has increased in recent years. While there is wide concern about the effects of EMR on humans and animals, the influence of EMR on plants is not well understood. In this study, we investigated the effect of EMR on the growth dynamics of Myriophyllum aquaticum (Parrot feather) by measuring the nanometric elongation rate fluctuation (NERF) using a statistical interferometry technique. Plants were exposed to 2 GHz EMR at a maximum of 1.42 Wm(-2) for 1 h. After continuous exposure to EMR, M. aquaticum plants exhibited a statistically significant 51 ± 16% reduction in NERF standard deviation. Temperature observations revealed that EMR exposure did not cause dielectric heating of the plants. Therefore, the reduced NERF was due to a non-thermal effect caused by EMR exposure. The alteration in NERF continued for at least 2.5 h after EMR exposure and no significant recovery was found in post-EMR NERF during the experimental period.

An optical interferometric technique for assessing ozone induced damage and recovery under cumulative exposures for a Japanese rice cultivar

Exposure to ozone (O₃) causes reduction both in the growth and yield of rice (Oriza sativa L.). Commonly used Chlorophyll fluorescent measurements are not sensitive enough for short term exposure of O₃ aiming an immediate assessments. Such a conventional method typically needs exposure over a few days to detect the influence. As an alternative method, we proposed a novel non-invasive, robust, real-time, optical Statistical Interferometric Technique (SIT) to measure growth at an accuracy of 0.1 nm with a commonly consumed Japanese rice cultivar, Koshihikari. In the present study, we have conducted a repetitive O₃ exposure experiment for three days under three different concentrations of 0 nl l^-1 (control), 120 nl l^-1, and 240 nl l^-1, to investigate the damage and recovery strengths. As a measure to assess the effect and recovery from three consecutive day exposures of O₃, we measured the elongation rate (nm mm^-1 sec^-1) every 5.5 sec for 7 hours, and it revealed nanometric elongation rate fluctuations or Nanometric Intrinsic Fluctuations (NIF). Comparing the standard deviation (SD) of normalized nanometric intrinsic fluctuations (NNIF), which was normalized by that before the exposure, we found that drastic reductions under both 120 nl l^-1 and 240 nl l^-1 O₃ concentrations. Reduction percentages were large under high O₃ concentration of 240 nl l^-1 indicating the possibility of irreversible effect. However exposure to 120 nl l^-1 of O₃ showed recovery on the 2^nd and 3^rd days. While SIT did reveal immediate effect based on an observation for a few hours, the visible foliar effect could be observed only after a week. Hence, the technique could provide a way for fast assessment of effect and recovery due to cumulative exposure of O₃ and hence the tolerance as well as the vitality of plant.

Expansion of the dynamic range of statistical interferometry and its application to extremely short- to long-term plant growth monitoring

In this study, we propose a method to expand the dynamic range of expansion or strain measurement using statistical interferometry. Statistical interferometry is a very accurate interferometric technique that is applicable to practical rough surface objects [Opt. Lett. 16, 883 (1991); J. Opt. Soc. Am. A 18, 1267 (2001)]. It is based on the statistical stability of a fully developed speckle field and was successfully applied to measure the growth of plants in our previous study [Environ. Exp. Bot. 64, 314 (2008); J. For. Res. 12, 393 (2007)]. However, the measurable range of the expansion of the object was restricted to less than one wavelength of the light used. Improvement of the dynamic range is confirmed experimentally in this work by introducing a large expansion up to 300 μm while keeping the precision of measurement high. Next, the improved system is applied to monitor plant growth from the subnanometric scale to several hundreds of micrometers under some environmental conditions. These features of the method make it especially worthwhile in botanical and agricultural studies.

Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps

A new approach to reconstructing the object wave front in phase-shifting interferometry with arbitrary unknown phase steps is proposed. With this method the actual phase steps are first determined from measured intensities with an algorithm based on the statistic property of the object phase distribution in the recording plane. Then the original object field is calculated digitally with a derived formula. This method is simple, accurate, and capable of retrieving the original object field, including its amplitude and phase distributions simultaneously, with arbitrary and unequal phase steps in a three- or four-frame method. The effectiveness and correctness of this approach are verified by a series of computer simulations for both smooth and diffusing surfaces.

Statistical interferometry based on a fully developed speckle field: an experimental demonstration with noise analysis

A novel interferometric method named statistical interferometry is proposed and studied. In the method, in contrast to the conventional deterministic interferometry, the complete randomness of the two interfering light fields, i.e., the random interference of the fully developed speckle fields, plays an essential role and is used as a standard of phase in a statistical sense. Preliminary experiments were conducted to verify the validity of the method, followed by a computer simulation. As an experimental result, the accuracy of the measurements of an out-of-plane displacement was confirmed up to lambda/800 by comparison with the heterodyne interferometer. The method has the advantage of simplicity of the optical system required, while at the same time providing high accuracy.

Spatial phase shifting in electronic speckle pattern interferometry: minimization of phase reconstruction errors

The advantages of spatial phase shifting (SPS) compared with temporal phase shifting in the field of electronic speckle pattern interferometry are described. Some periodic phase reconstruction errors occurring in SPS are discussed. It is shown that these errors become minimal for a spatial phase-shift angle of 2pi/3. Furthermore, a modified phase reconstruction formula is presented by which the noise in the reconstructed phase map is reduced.