Calibration
1. Process
a) Assuming velocity of and length scale of
b) Magnification
I. Region imaged (R.O.I.) = 10cm x 10 cm
II. Sensor Size (S.S.) = 1cm x 1cm
III. Magnification (M) = 1 cm/10 cm =0.1
2. Illumination and Imaging
a) Laser Sheet Thickness T = 1mm
b) Laser Sheet Width 𝐿𝑊 = 11 cm
c) Lenses to be used:
i. 𝑓1 = -10 mm (plano-concave lens)
ii. 𝑓2 = 10 mm
d) F# of the camera lens = 2.8
𝑓 2
e) Depth of focus = 4(1 + 𝑀−1 )2 (𝐷) 𝜆
𝑓
= 2018705.92 x 10−9 mm
where 𝜆 = 532 𝑛𝑚 , (𝐷) = 𝐹#
3. Particles
a) Particle size in 𝜇m ⅆ𝑝 = 10
b) Particle density 𝜌 = 1.1 g/cc
c) Free fall velocity of the particles 𝑣𝑓𝑓 =
d)
e)
f)
g)
2𝑟 2(𝜌−𝜌𝑝 )𝑔
9𝜂
= 5 x 10−4 m/sec
where 𝜂 = 10−3
Ratio of the velocity scales 𝑣𝑓𝑓 /𝑣𝑓 = 2.5 x 10−4
where 𝑣𝑓 (friction velocity) = 2 m/sec
Particle number density N = 2.93 x 109
Amount of seeding particles required = 1.65 grams
Physical image size of the particle Mⅆ𝑝 = 1 𝜇m
𝑓
h) Diffraction limited spot size ⅆ𝑠 = 2.44(1 + 𝑀) 𝐷 𝜆 = 4 x 10−6 m
i) Effective particle diameter d = √𝑀2 ⅆ𝑝2 + ⅆ𝑠2 = 4.123 x 10−6 m
4. Imaging and Timing
a) Interrogation area chosen for processing 𝑙 2 = I.A.
b) Time of separation required to get l/4 = 8 px / (1 m/sec) = 0.8 ms
c) Light sheet thickness out of plane motion considerstion
d) Gradients consideration
e) Exposure time = 0.1 ms
5. Observations on Images
a) Particle number density
b) Particle diameter
c) Homogeneity of images
d) Out of plane loss of particles
e) SNR of the images
6. Processing
a) Choice of the algorithm = fft
b) Vector field quality
c) Outlier detection
7. Errors