Table 1
Comparison of Uncertainty
${\mathrm{\Sigma}}_{\mathbf{f},p1}$
(
${\mathrm{nm}}^{\mathrm{1}}$
) of Unimodal Particle Size Distribution Reconstructed with use of Regularized LeastSquares and Constrained Regularized LeastSquares Methods for Various p Values and for Various L Matrices
 Inverse Method 


L—Identity Matrix 
L—First Derivative 
L—Second Derivative 
L—Third Derivative 

p (%)  RLS  CRLS  RLS  CRLS  RLS  CRLS  RLS  CRLS 

0.0 
$2.67\times {10}^{18}$

$3.22\times {10}^{18}$

$4.32\times {10}^{18}$

$4.65\times {10}^{18}$

$4.67\times {10}^{18}$

$4.57\times {10}^{18}$

$4.72\times {10}^{18}$

$4.63\times {10}^{18}$

2.5  0.000443  0.000545  0.000351  0.000395  0.000951  0.000264  0.085627  0.001455 
5.0  0.000604  0.000714  0.001508  0.000886  0.014054  0.000812  0.241890  0.002354 
7.5  0.000712  0.000763  0.043188  0.001516  0.043476  0.001521  0.450080  0.002335 
Table 2
Comparison of Deviation
${\mathrm{\Delta}}_{\mathbf{f},p1}$
(
${\mathrm{nm}}^{\mathrm{1}}$
) of Unimodal Particle Size Distribution, Reconstructed with Use of Regularized LeastSquares and Constrained Regularized LeastSquares Methods, from Test Particle Size Distribution for Various p Values and for Various L Matrices
 Inverse Method 


L—Identity Matrix 
L—First Derivative 
L—Second Derivative 
L—Third Derivative 

p (%)  RLS  CRLS  RLS  CRLS  RLS  CRLS  RLS  CRLS 

0.0  0.002173  0.002017  0.000906  0.000538  0.000980  0.000595  0.001053  0.000444 
2.5  0.001115  0.000671  0.001069  0.000645  0.001149  0.000754  0.012059  0.000331 
5.0  0.001194  0.000817  0.001392  0.001007  0.001785  0.000686  0.020425  0.000849 
7.5  0.001293  0.001023  0.004439  0.001170  0.006477  0.000504  0.033867  0.000900 
Table 3
Comparison of Uncertainty
${\mathrm{\Sigma}}_{\mathbf{f},p2}$
(
${\mathrm{nm}}^{\mathrm{1}}$
) of Bimodal Particle Size Distribution Reconstructed with Use of Regularized LeastSquares and Constrained Regularized LeastSquares Methods for Various p Values and for Various L Matrices
 Inverse Method 


L—Identity Matrix 
L—First Derivative 
L—Second Derivative 
L—Third Derivative 

p (%)  RLS  CRLS  RLS  CRLS  RLS  CRLS  RLS  CRLS 

0.0 
$2.90\times {10}^{18}$

$3.14\times {10}^{18}$

$4.06\times {10}^{18}$

$4.13\times {10}^{18}$

$4.91\times {10}^{18}$

$4.31\times {10}^{18}$

$4.75\times {10}^{18}$

$4.22\times {10}^{18}$

2.5  0.000443  0.000545  0.000351  0.000395  0.000951  0.000264  0.085627  0.001455 
5.0  0.000612  0.000731  0.001277  0.000842  0.003640  0.000746  0.258470  0.002053 
7.5  0.000852  0.000879  0.030492  0.001388  0.037157  0.001446  0.204980  0.002412 
Table 4
Comparison of Deviation
${\mathrm{\Delta}}_{\mathbf{f},p2}$
(
${\mathrm{nm}}^{\mathrm{1}}$
) of Bimodal Particle Size Distribution, Reconstructed with use of Regularized LeastSquares and Constrained Regularized LeastSquares Methods, from Test Particle Size Distribution for Various p Values and for Various L Matrices
 Inverse Method 


L—Identity Matrix 
L—First Derivative 
L—Second Derivative 
L—Third Derivative 

p (%)  RLS  CRLS  RLS  CRLS  RLS  CRLS  RLS  CRLS 

0.0  0.002229  0.002040  0.000796  0.000790  0.000812  0.000810  0.001118  0.000858 
2.5  0.001173  0.000801  0.001110  0.000833  0.001033  0.000918  0.005639  0.001133 
5.0  0.001211  0.000856  0.001323  0.001012  0.001138  0.000963  0.024739  0.001378 
7.5  0.001231  0.000928  0.003163  0.001208  0.001730  0.001059  0.038134  0.001551 