Apparatus for a dynamic multi-axis heterodyne interferometric vibrometer

The invention described herein may be manufactured, used, sold, imported, and/or licensed by or for the Government of the United States of America.

The present invention relates to coherent optical vibration sensing, specifically to measure dynamic multi-axis motion of an object.

Coherent optical vibration sensors have been investigated for use in numerous applications including strain measurements, equipment diagnostics, medical imaging, and seismic sensing. Various techniques have been utilized to observe surface motion including heterodyne laser Doppler vibrometry (e.g., U.S. Pat. No. 4,834,111 to Khanna et al.) for observation of surface velocity in the axial dimension of the interrogation beam, shearography (e.g., U.S. Pat. No. 5,011,280 to Hung) for observation of the gradient of displacement in two dimensions, electronic speckle pattern interferometry (e.g., U.S. Pat. No. 4,018,531 to Leendertz) for dynamic out of plane contour observation, and heterodyne digital image correlation for out-of-plane displacement and rotation (U.S. Pat. No. 9,651,477 to Libbey et al.). Techniques to observe the image and Fourier planes simultaneously to measure in-plane translation and out-of-plane rotation have been demonstrated using direct detection and holographic techniques. (See, e.g., Kelly, D. P., Hennelly, B. M., & Sheridan, J. T. (2005), “Magnitude and direction of motion with speckle correlation and the optical fractional Fourier transform,” Applied optics, 44(14), 2720-2727; and Bhaduri, B., Quan, C., Tay, C. J., & Sjodahl, M. (2010), “Simultaneous measurement of translation and tilt using digital speckle photography,” Applied optics, 49(18), 3573-3579.)

The techniques listed are generally used for observation of one or two degrees of freedom. Variations using multiple coherent beams (e.g., U.S. Pat. No. 7,242,481 B2 to Shpantzer et al.) have been used to observe three degrees of freedom, or three-dimensional deformations. (See, also, Rajshekhar, G., Gorthi, S. S., & Rastogi, P. (2011), “Simultaneous measurement of in-plane and out-of-plane displacement derivatives using dual-wavelength digital holographic interferometry,” Applied optics, 50(34), H16-H21; Alvarez, A. S., Manuel, H., Santoyo, F. M., & Anaya, T. S. (2014), “Strain determination in bone sections with simultaneous 3D digital holographic interferometry,” Optics and Lasers in Engineering, 57, 101-108; and Saucedo-A, T., De la Torre-Ibarra, M. H., Santoyo, F. M., & Moreno, I. (2010), “Digital holographic interferometer using simultaneously three lasers and a single monochrome sensor for 3D displacement measurements,” Optics express, 18(19), 19867-19875.) It is of interest to observe in-plane and out-of-plane components of motion using a single interrogation beam.

The current invention combines elements of heterodyne Doppler vibrometers, holographic sensors, and digital image correlation to acquire light scattered from a dynamic surface. The apparatus simultaneously collects magnitude and phase of a light field at the image and Fourier planes. Information contained in the magnitude and phase of these complex measured fields provides the ability to observe five degrees of freedom including in-plane translation, out-of-plane rotation, and out-of-plane displacement using a single coherent illumination source.

The invention observes a dynamic object by mixing optical field data with heterodyne reference beams and collecting these combined fields at image and Fourier planes. The apparatus utilizes a receive Mach-Zehnder interferometer in which each segment contains a different optical configuration. One segment produces a focused image of the electric field scattered off the object while the other segment produces an optical Fourier transform of the electric field scattered off the object, these are the receive paths. The image and Fourier planes are simultaneously sensed on a pixelated focal plane array, but are separable because each segment of the receive interferometer is orthogonally polarized and modulated at distinct frequencies. Two reference paths contain acousto-optic modulators to create two intermediate frequencies and optical components to orthogonally polarize these paths. These two reference light paths are recombined and aligned on a common exit path. Mixing the reference and measurement fields on a high-speed focal plane array creates an interference pattern with two carrier frequencies. Each carrier contains information pertaining to one segment of the receive interferometer. Each segment is Doppler shifted due to the object's time varying path length in the axial direction of the interrogation beam. In the segment representing the Fourier plane, the measurement field shifts laterally due to out-of-plane rotation while the phase contains a linear variation proportional to the object's in-plane translation and an additional Doppler shift due to out-of-plane rotation. In the segment representing the image plane, the measurement field shifts laterally due to in-plane translation while the phase contains a linear variation proportional to the object's out-of-plane rotation.

Additional advantages and features will become apparent as the subject invention becomes better understood by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein:

FIG. 1 shows an exemplary laboratory sensor schematic for a multi-axis heterodyne interferometric vibrometer.

FIG. 2 shows an exemplary block diagram illustrating the sensor process of the multi-axis heterodyne interferometric vibrometer shown in FIG. 1 .

An exemplary multi-axis heterodyne interferometric vibrometer is represented in FIG. 1 , and its exemplary process is shown in FIG. 2 . FIG. 1 shows schematic of the multi-axis heterodyne interferometric vibrometer with a dynamic diffuse-scatterer for the target. Specifically, shown in FIG. 1 are: 101 , 532 nm laser source; 102 , 50:50 beam splitter; 103 , beam collimator; 104 , mirror; 105 , dynamic diffuse scatterer; 106 , 100 mm focal length collecting lens; 107 , polarizing filter; 108 , 50:50 beam splitter; 109 , half wave plate; 110 , mirror; 111 , 125 mm focal length converging lens; 112 , mirror; 113 , 100 mm focal length converging lens; 114 , 50:50 polarizing beam splitter; 115 , 50:50 beam splitter; 116 , 10 kHz acousto-optic modulator (AOM); 117 , mirror; 118 , half wave plate; 119 , 15 kHz AOM; 120 , mirror; 121 , 50:50 polarizing beam splitter; 122 , −25 mm focal length diverging lens; 123 , 70:30 beam splitter; 124 , 512×512 pixel focal plane array sampling 40,000 frames per second (FPS); 125 , trans-impedance amplifier; 126 , computer. FIG. 2 shows the block diagram corresponding to the sensor schematic in FIG. 1 .

An exemplary laser source is a horizontally polarized laser 101 . A splitter 102 divides the source into a probe and reference beams. In the probe beam path, a series of lenses 103 collimate the beam, and mirror 104 directs the beam to an object 105 . The object's surface is rough on the scale of an optical wavelength and vibrates as a rigid body. The probe beam scatters from the moving object 105 ; the resulting field now has a random spatial phase, amplitude, and polarization. The purpose of the invention is to capture the phase and amplitude information in order to track the surface's position. As the object moves, a Doppler phase shift is imparted due to the optical path length change near the object plane 105 , while linear phase shifts and field translation occur due to out-of-plane rotation and in-plane translation. The optical field at the object is modified by a phase associated with the new position of the object,

u o ⁡ ( ξ , η , z ) → u o ⁡ ( ξ - Δ ⁢ ⁢ ξ , η - Δ ⁢ ⁢ η , z ) ⁢ e j ⁢ ⁢ 4 ⁢ π λ ⁢ ( θ ⁢ ⁢ ξ + γ ⁢ ⁢ η ) ⁢ e - j ⁢ ⁢ 4 ⁢ ⁢ π λ ⁢ Δ ⁢ ⁢ z , ( 1 )

where ξ,η are the in-plane coordinates in the object plane; z is the out-of-plane coordinate; Δξ, Δη, and Δz are the object displacements respectively; θ, γ are the components of rotation about the η, ξ axes; and λ is the optical wavelength. u o represents a random, complex, optical field caused by scattering from the object.

Some of the resulting scattered radiation is collected by a single 100 mm focal length lens 106 . The field propagates through a dichroic polarizing filter 107 where the vertically polarized radiation is absorbed. A splitter 108 divides the field into two segments. A half wave plate 109 rotates one segment's polarization 90 degrees creating a vertically polarized field. A mirror 110 directs the vertically polarized field to a 125 mm focal length lens 111 . Lens 111 converges the vertically polarized field and produces an image of the Fourier plane produced by lens 106 . The vertically polarized, converging field propagates to the polarizing beam splitter 114 which combines the vertically polarized field with a horizontally polarized field from the splitter 108 . The horizontally polarized field leaves splitter 108 and is redirected by mirror 112 to a 100 mm focal length lens 113 . Lens 113 produces an image of the image plane produced by lens 106 . Other combinations of focal lengths may be used as long as certain criteria are met. The focal length of lens 106 should be equivalent to ½ the distance between lens 106 and object 105 . In this case, a virtual image plane is produced at two focal lengths from lens 106 and a virtual Fourier plane is produced at one focal length from lens 106 . The focal length of lens 111 should be chosen to image the virtual Fourier plane on the focal plane array, 124 . The focal length of lens 113 should be chosen to image the virtual image plane on the focal plane array, 124 . The combined fields leave splitter 114 and propagate to a non-polarizing splitter 123 as a combined probe field.

Following initial propagation through the beam splitter 102 , the reference beam propagates to a splitter 115 dividing the beam into two reference beams. Each beam propagates through an acousto-optic modulator (AOM), 116 and 119 . AOM 116 shifts the frequency by one carrier frequency ω f , upshifting the optical carrier by 10 kHz. A mirror 117 directs the beam to a half wave plate 118 which rotates the polarization 90 degrees, creating a vertically polarized beam. The beam then propagates to a polarizing beam splitter 121 . AOM 119 shifts the frequency by another carrier frequency ω i , upshifting the optical carrier by 15 kHz. Other combinations of carrier frequencies may be chosen, provided the FPA frame rate meets the Nyquist sampling criteria. A mirror 120 directs the beam to the polarizing beam splitter 121 that combines the beams. The combined reference beam propagates to a lens 122 which expands the beam. The reference beam propagates to the non-polarizing splitter 123 where it is combined with the probe field from the polarizing beam splitter 114 .

Splitter 123 combines the reference beam and probe field and projects them to the focal plane array 124 which transduces the irradiance of the field into an electrical charge proportional to the irradiance. A trans-impedance amplifier circuit 125 converts charge from the focal plane array 124 into a digital representation of the irradiance on a computer 126 . Elements 124 , 125 , and 126 are capable of repeating the irradiance collection process to capture the dynamic changes of the object and carrier frequencies imposed on the reference beam thus producing image frames. Each frame, representing irradiance, can be described by

I ( x,y,t )=| R f | 2 +|R i | 2 +|M f ( x,y,t )| 2 +|M i ( x,y,t ) 2 +2| R f ∥M f ( x,y,t )|cos [ω f t+ψ f ( x,y,t )]+2| R i ∥M i ( x,y,t )|cos [ω i t+ψ i ( x,y,t )],  (2)

where |R f |, |R i | are the reference segments' magnitudes, and ω f , ω i are the reference segments' carrier frequencies. |M f |, |M i | represent the Fourier transform and image magnitudes of object 105 respectively. ψ f , ψ i represent the Fourier transform and image phases of object 105 respectively; these phase signals are carried on ω f and ω i respectively. Polarization is essential to this invention because the mixed signal terms, 2|R f ∥M f |cos[ω f t+ψ f ] and 2 |R i ∥M i |cos[ω i t+ψ i ], are separable due to their unique carrier frequency. Equally important is that the measurement is not confounded by cross terms: R f does not mix with M i and likewise R i does not mix with M f . The essence of this invention is that the irradiance data is separable into Fourier plane complex-field data and image plane complex-field data.

|M f | shifts laterally due to out-of-plane rotation while |M i | shifts laterally due to in-plane translation. ψ f contains Doppler spatially-uniform shift due to out-of-plane displacement and out-of-plane rotation of the object 105 and contains a linear spatial phase term due to the object's in-plane translation. ψ i contains Doppler shift due to out-of-plane displacement of the object 105 and a linear spatial phase term due to the out-of-plane rotation.

It is obvious that many modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as described.