Goodwill and Intangible Assets, Net (Narrative) (Details) - USD ($) $ in Thousands	3 Months Ended
	Apr. 02, 2017	Apr. 03, 2016	Jan. 02, 2017	Jan. 01, 2017
Goodwill and Intangible Assets Net [Line Items]
Reporting Unit, Percentage of Fair Value in Excess of Carrying Amount			20.00%
Long-term terminal growth rates for reporting units	0.00%
Change in any one of the input assumptions for the various reporting units	10.00%
Goodwill	$ 2,332,533			$ 2,247,966
Total amortization expense related to finite-lived intangible assets	17,000	$ 18,600
Future Amortization Expense, Year One	51,200
Future Amortization Expense, Year Two	66,500
Future Amortization Expense, Year Three	54,900
Future Amortization Expense, Year Four	46,700
Future Amortization Expense, Year Five	34,000
Finite-Lived Intangible Assets, Net	384,544			349,640
Intangible assets, net	$ 455,128			420,224
Minimum [Member]
Goodwill and Intangible Assets Net [Line Items]
Discount rates for reporting units	9.00%
Maximum [Member]
Goodwill and Intangible Assets Net [Line Items]
Discount rates for reporting units	13.50%
Patents [Member]
Goodwill and Intangible Assets Net [Line Items]
Gross amortizable intangible assets	$ 39,906			39,901
Less: Accumulated amortization	33,071			32,408
Finite-Lived Intangible Assets, Net	6,835			7,493
Trade Names And Trademarks [Member]
Goodwill and Intangible Assets Net [Line Items]
Gross amortizable intangible assets	43,371			40,086
Less: Accumulated amortization	24,990			24,017
Finite-Lived Intangible Assets, Net	18,381			16,069
Licensing Agreements [Member]
Goodwill and Intangible Assets Net [Line Items]
Gross amortizable intangible assets	50,804			57,767
Less: Accumulated amortization	40,279			46,507
Finite-Lived Intangible Assets, Net	10,525			11,260
Core Technology [Member]
Goodwill and Intangible Assets Net [Line Items]
Gross amortizable intangible assets	292,252			304,187
Less: Accumulated amortization	222,371			233,720
Finite-Lived Intangible Assets, Net	69,881			70,467
Customer Relationships [Member]
Goodwill and Intangible Assets Net [Line Items]
Gross amortizable intangible assets	411,165			383,303
Less: Accumulated amortization	207,297			213,062
Finite-Lived Intangible Assets, Net	203,868			170,241
In-process Research and Development [Member]
Goodwill and Intangible Assets Net [Line Items]
Gross amortizable intangible assets	79,698			78,515
Less: Accumulated amortization	4,644			4,405
Finite-Lived Intangible Assets, Net	$ 75,054			74,110
Informatics [Member]
Goodwill and Intangible Assets Net [Line Items]
Goodwill			$ 211,000
Medical Imaging Business [Member]
Goodwill and Intangible Assets Net [Line Items]
Disposal Group, Including Discontinued Operation, Consideration				$ 276,000