1564 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 12, NO. 4, AUGUST 2016 Experiments on a Simple Setup for Two-Step Quadrature Phase-Shifting Holography Wenjing Zhou, Hongbo Zhang, Yingjie Yu, and Ting-Chung Poon, Senior Member, IEEE Abstract—We report a simple setup for two-step quadra- ture phase-shifting holography that could be useful and suitable for industrial applications. Only two on-axis holo- grams are captured with the system and a complex holo- gram is formed from the two holograms. Autocorrelation is used to quantify the quality of all the reconstructed images from the holograms. We have tested a transparent sample as well as a reflective sample to validate this simple setup. Index Terms—Complex hologram, digital on-axis holo- graphy, π/2 phase-shifting, twin image noise. I. I NTRODUCTION D IGITAL holography can record and reconstruct the inten- sity and the phase of a three-dimensional (3-D) object [1]–[2]. It has been applied to many disciplines such as 3-D microscopy, fluid mechanics, and particle dynamics [3]–[6]. Phase-shifting holography (PSH) is often used to reconstruct the complex wave of an object [7]–[10] on the charge cou- pled device (CCD) recording plane. Because the twin image noise always could not be avoided in single on-axis holo- gram, PSH is often used in practice to obtain the complex field of the object without twin image noise. However, at least three holograms are needed to be recorded. Quadrature PSH only needs to record two holograms but the intensities of the object and reference waves are still needed to be measured or calculated [11]–[12]. Recently, we have proposed a very simple method to extract the complex amplitude of the object by using only two quadrature phase-shifted holograms with- out other recordings or calculations. Some simulations have been performed [13]. In this paper, we perform some actual optical experiments on the proposed method and show that experimental results confirm our previous simulation results. In the proposed method, there is no twin image noise upon Manuscript received September 01, 2015; revised October 19, 2015; accepted November 17, 2015. Date of publication December 01, 2015; date of current version August 04, 2016. This work was supported in part by the Young Scientists Fund of the Natural Science Foundation of China under Grant 61107004 and in part by the Natural Science Foundation of China under Grant 61575119. Paper no. TII-15-1363. W. Zhou is with the Department of Precision Mechanical Engineering, Shanghai University, Shanghai 200072, China, and also with the Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA 24060 USA (e-mail: wjzz1331@vt.edu). H. Zhang and T.-C. Poon are with the Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA 24060 USA (e-mail: hbzhang@vt.edu; tcpoon@vt.edu). Y. Yu is with the Department of Precision Mechanical Engineering, Shanghai University, Shanghai 200072, China (e-mail: yingjieyu@staff.shu.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TII.2015.2504843 holographic reconstruction but some residual background dc noise exists. Auto-correlation of reconstructed images from holograms is used to quantify the quality of the obtained images. II. PRINCIPLE FOR THE GENERATION OF COMPLEX HOLOGRAM AND SIMULATION RESULTS We first obtain two quadrature on-axis holograms as follows: I 1 = |Q + R| 2 = |Q| 2 + |R| 2 + 2R Re[Q] (1) I 2 =   Q + e jπ/2 R    2 = |Q| 2 + |R| 2 +2R Im[Q] (2) where Q and R are the complex amplitude of the object light and the amplitude of the reference light on the CCD recording plane, respectively. From the two holograms, we then obtain two complex holograms as follows: I +j = I 1 + jI 2 =(1 + j )(|Q| 2 + |R| 2 )+ 2RQ =(1 + j )R 2 (β + 1) + 2RQ (3) and I -j = I 1 - jI 2 = (1 - j )(|Q| 2 + |R| 2 )+2RQ ∗ = (1 - j )R 2 (β + 1) + 2RQ ∗ (4) where β = |Q| 2 /R 2 and we have assumed that the reference amplitude is real and constant for simplicity. In practice, this can be done by providing a plane wave as a reference beam. Note that (3) and (4) contain the object wave and its conjugate on the recording plane, respectively. Each of the equation does not contain any twin image information but has a zeroth-order term. So, if we assume β ≤ 1, i.e., the intensity of the refer- ence wave is much larger than that of the object wave, the two complex holograms become I +j =(1 + j )R 2 + 2RQ (5) and I -j = (1 - j )R 2 +2RQ ∗ . (6) Note that we now basically have the complex object wave and its conjugate in addition to a constant in (5) and (6), respec- tively. In [13], for β =0.5, 0.2, 0.1, we have applied cross correlation function to evaluate the quality of the reconstructed images compared with the original Lena image. According 1551-3203 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.