# Solar Acoustic Holograms

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### Transcript of Solar Acoustic Holograms

Solar Acoustic Holograms Tsing Hua University, TaiwanJanuary 2008, Tucson Dean-Yi Chou

MotivationIs it feasible to apply the principle of optical holography to a system of solar acoustic waves and active regions?

ContentsPrinciple of optical holography.Concept of acoustic holography of active regions.Construct 3-D wave fields of the magnetic region from the acoustic hologram.Set up a simplified model to compute acoustic holograms of magnetic regions. 1. analogies and differences between two 2. difficultiesChallenges and prospects.

Hologram (interference pattern)(time average)

Construction of Waveshologramdiffraction field(Gabors in-line holgram)

Acoustic waves on the Sun

solar surfaceinterference patternSolar Acoustic Waves + Active Region(acoustic power map)perturbed region

Optical HolographySolar Acoustic Holographyreference waveobjecthologramp-mode wavemagnetic regionacoutsic power mapAnalogies(coming from below)(near the surface)(on the surface)

Questions:1. Can we detect the inference pattern (hologram) due to a magnetic region on the surface?2. Can we use the observed hologram to construct the 3-D image of the magnetic region?

Optical HolographySolar Acoustic Holography1. monochromatic 5. far field approximation4. single reference wave finite band width wavelength ~ dimension of object ~ distance to hologram* multiple incident wavesDifferences2. no boundary trapped in cavities3. straight ray path curved ray path

If the width of power spectrum of a wave field is , the cohernt time of waves iscoherent time of waves: central frequency: period of central frequencyexample3.3 mHz0.2 mHz (FWHM = 0.47 mHz)2.6

solar surfacetrapped in cavitiescurved ray pathmultiple incident waves2. Waves are approximately vertical near the surface1. Refracted waves from the lower turning point are ignored. sa a s

Multiple Incident WavesIf incident waves are, total waves are Intensity of hologramcross termsIf different waves are uncorrelated, the contribution from cross terms is small. Total interference is the sum of interference of individual wave.interference termSummation of interferences of different waves reduces the visibility of fringes.

1. Set up a simplified model for scattering of acoustic waves by a magnetic region. 2. Solve for the scattered waves. 3. Compute the interference pattern (hologram) between incident wave and scattered wave.4. Study the influence of various parameters on the hologram.5. Compute the constructed wave field by illuminating the hologram with a reference wave.Model Study

Assume unperturbed medium is uniform, and the wave equation isAssume the interaction between waves and magnetic regions is described by sound-speed perturbations:time independent Wave equation becomesSource of scatteringWave Equation

Solution of Scattered Wavescattered wave with Greens function and Born approximation wave equationtotal solutionexpressed in terms of Fourier components

HologramIntensity of the hologram is the time average of interference Interference termNeed a model for spatial dependence of

A Simplified Model for assumptions:1. Consider only one upward wave mode and its reflected wave at the surface. 2. Assume the free-end boundary at the surface. interference termnormalized interference term (related to fringe visibility)3. Simple dispersion relation:

Normalized Interference Term (fringe visibility)Effects of parameters on holograms1. coherent time of incident waves3. size of the perturbed region4. depth of the perturbed region2. wavelength5. angle of incidence

Effects of Coherent Time of Incident WavesSetup of incident wave3. Modes with a Gaussian power spectrum centered at 3.3 mHz, with different widths. 1. Waves propagate vertically: 2. Dispersion relation: 4. coherent timePerturbed region1. Uniform cylinder with 2. diameter = 9.6 Mm, vertical extent = 4.8 Mm, depth = 12 Mm3.3 mHz,14.7 Mm (l=300),48.5 km/s

Effects of Coherent Time0.2 mHz (FWHM = 0.47 mHz)line width

Effects of Wavelength3.3 mHz,0.2 mHz uniform cylinder with diameter = 9.6 Mm, vertical extent = 4.8 Mm, depth = 12 Mmwavelength

Effects of Angle of IncidenceAt 5Mm depth, the angle of incidence is about for at 3.3 mHz.for at 3.3 mHz.Waves with different phase velocities have different angles of incience. For example:

Effects of Angle of Incidence (cont.)3.3 mHz,0.2 mHz, uniform cylinder with diamter = 9.6 Mm, vertical extent = 4.8 Mm, depth = 12 Mm14.7 Mm (l=300)incident angle

Construction of Wave Fields from HologramsIlluminate the hologram by a vertically-propagating monochromatic wave.hologram on the surface

Advantages of digital hologramsDC signal2. Disentangling wave fields of virtual and real images.1. DC signals are removed to enhance the interference pattern.

hologram on the surfaceDiffraction waves are computed by the Kirchhoff intergralreplaced by

Constructed wave field205 Mm30 MmIncident angle = 0Mmdepth = 30 Mm

Constructed wave fieldIncident angle = 0 deg.Depth = 30 MmIncident angle = 0 deg.Depth = 12 Mm

Constructed wave fieldIncident angle = 0 deg.Depth = 30 MmIncident angle = 10 deg.Depth = 30 Mm

Effects of Multiple Incident Waves 1. Weaken holograms2. Distort and weaken constructed wave fields

The maximum occurs at . 1. Signals of holograms are weak. Challenges in detecting interference fringes2. Interference fringes are contaminated by suppression of acoustic power in magnetic region. Fluctuation of 1000 MDI Dopplergrams is about 10%.1% for the 2nd and 3rd fringes ifRemove suppression by an empirical relation of power vs. field strength. Search for interference fringes outside magnetic regions. 3. Find an optimal filter to detect interference fringes.

power map before correctionpower map after correctionmagnetic fieldPower vs. B field1024 MDI FD images

phase-velocity-filtered power map magnetic fieldpower map1024 MDI FD imagesphase-velocity-filtered power map (3.3mHz/300)(3.3mHz/400)

power map before correctionpower map after correctionmagnetic fieldPower vs. B field512 MDI HR images

Challenges in Constructed 3D Wave Fields2. Is there a better way to construct 3D wave fields? How to disentangle wave fields of virtual and real images and obtain the 3D structure of the magnetic region?

Improvement in computing interference fringes1. A better model to compute scattered waves. 2. Study of simulation datainteraction between waves and B fieldsmore realistic dispersion relationProspectsBetter DataHinode & HMI

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