Reduction of Truncation Errors in Planar, Cylindrical, and Partial Spherical Near-Field Antenna Measurements

Table 1

Determination of the spectral reliable regions based on geometrical optics for each type of measurement setup.

Measurement set-up	Maximum validity angles	Spectral reliable region
PNF measurement	𝜃𝑥=arctan((𝐿𝑥−𝐴𝑥)/2𝐷);𝜃𝑦=arctan((𝐿𝑦−𝐴𝑦)/2𝐷)	{𝑘2𝑥/(𝑘sin𝜃𝑥)2+𝑘2𝑦/𝑘2<1}∩{𝑘2𝑥/𝑘2+𝑘2𝑦/(𝑘sin𝜃𝑦)2; <1}
CNF measurement	𝜃𝑦=arctan((𝐿𝑦−𝐴𝑦)/2𝐷)	{|𝑘𝑦|<𝑘sin𝜃𝑦}
SNF measurement with polar truncation	𝜃𝑣=𝜃𝑡−arcsin(𝑟0/𝐷)∗	{𝑘2𝑥+𝑘2𝑦<(𝑘sin𝜃𝑣)2}
SNF measurement with spherical ring truncation	𝜃𝑣1=𝜃𝑡1−arcsin(𝑟0/𝐷);𝜃𝑣2=𝜃𝑡2+arcsin(𝑟0/𝐷)∗	{𝑘2𝑥+𝑘2𝑦<(𝑘sin𝜃𝑣1)2}∩{𝑘2𝑥+𝑘2𝑦>(𝑘sin𝜃𝑣2)2}
SNF measurement with azimuthal truncation	𝜙𝑣1=𝜙𝑡1+arcsin(𝑟0/𝐷);𝜙𝑣2=𝜙𝑡2−arcsin(𝑟0/𝐷)∗	{𝑘𝑦>𝑘𝑥⋅tan𝜙𝑣1}∩{𝑘𝑦<𝑘𝑥⋅tan𝜙𝑣2}
SNF measurement with sectorial truncation	𝜃𝑣1=𝜃𝑡1−arcsin(𝑟0/𝐷);𝜃𝑣2=𝜃𝑡2+arcsin(𝑟0/𝐷)∗	{𝑘2𝑥+𝑘2𝑦<(𝑘sin𝜃𝑣1)2}∩{𝑘2𝑥+𝑘2𝑦>(𝑘sin𝜃𝑣2)2}
	𝜙𝑣1=𝜙𝑡1+arcsin(𝑟0/𝐷);𝜙𝑣2=𝜙𝑡2−arcsin(𝑟0/𝐷)∗	∩{𝑘𝑦>𝑘𝑥⋅tan𝜙𝑣1}∩{𝑘𝑦<𝑘𝑥⋅tan𝜙𝑣2}

* 𝑟0=(𝟏/𝟐)√𝐀𝟐𝐱+𝐴2𝑦.