We present a generalized perspective for "reduced" invisibility cloaks, which formulates a general way to "reduce" the cloak so that it can be realized more easily. We show explicitly that several published reduced cloak designs are in fact special cases of a more general transformation. Furthermore, we showed that a cylindrical reduced cloak is linked to a cylindrical isotropic inhomogeneous object by exactly the coordinate transformation that one applies on an ideal cloak. This perspective also suggests an alternative but easier way to calculate the scattering properties of the reduced cloaks. DOI: 10.1103/PhysRevB.80.085112 PACS number͑s͒: 41.20.Jb, 42.25.Fx, 42.79.Ϫe, 42.25.Gy Transformation optics 1,2 is a powerful and versatile theoretical tool that enables the design of various kinds of novel metamaterial devices. The most celebrated example is the invisibility cloaks. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] Other examples include field concentrators, 19 field rotators, 20-22 electromagnetic wormholes, 23 impedance-matched hyperlenses, 24 field shifters, 25,26 anticloaks, 27 cylindrical superlenses, 28 superscatterers, 29 superabsorbers, 30 and remote cloaks ͑or invisibility umbrellas͒. 31,32 However, the experimental fabrication of these novel devices requires sophisticated man-made metamaterial, which may not be always feasible to make. For this reason, researchers have attempted to "reduce" the complexity of the required constitutive parameters. The functionalities of these reduced devices, such as the reduced cloak, 3,5-7 are slightly less perfect compared to the original ideal devices, but they are designed to perform satisfactorily while having the advantage that they are much easier to fabricate. Indeed, the "reduced devices" will become those that shall be useful for real applications as the ideal devices are probably too difficult or expensive to make. So, there is a good reason that much effort 8,9,11-13 has been devoted to study the reduced cloaks. For example, a reduced cloak working in the microwave frequency was realized experimentally in 2006. 5 More recently, the "ground-plane cloak" 16 ͑also known as the "one-dimensional cloak 14,26 "͒, which has a broad working frequency spectrum, was also realized.For simplicity, we shall only consider the two dimensional case in this paper. The spatially varying constitutive parameters for the transverse electric ͑TE͒ ideal cloak are given bywhere f͑r͒ is the mapping function. The constitutive parameters for transverse magnetic ͑TM͒ ideal cloak can be obtained by making the substitution ͕ r → r , → , z → z ͖ in ͑1͒. By varying the functional form, we can achieve a varieties of functionalities such as the concentrator 21 ͑or the impedance-matched hyperlens 24 ͒, the anticloak 27 and the superscatterer, 29 cylindrical superlenses, 28 etc. However, these parameters involve spatially varying, anisotropy permittivity, and permeability, which can be formidably difficult to fabricate. Consequently, it is essential for one to "reduce" or ...