Goodwill and Intangible Assets, Net (Narrative) (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jul. 02, 2017	Jul. 03, 2016	Jul. 02, 2017	Jul. 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%
Change in any one of the input assumptions for the various reporting units			10.00%
Goodwill	$ 2,356,690		$ 2,356,690			$ 2,247,966
Total amortization expense related to finite-lived intangible assets	17,500	$ 18,400	34,600	$ 37,000
Future Amortization Expense, Year One	34,700		34,700
Future Amortization Expense, Year Two	69,100		69,100
Future Amortization Expense, Year Three	57,500		57,500
Future Amortization Expense, Year Four	49,200		49,200
Future Amortization Expense, Year Five	36,300		36,300
Finite-Lived Intangible Assets, Net	382,475		382,475			349,640
Intangible assets, net	453,059		$ 453,059			420,224
Minimum [Member]
Goodwill and Intangible Assets Net [Line Items]
Long-term terminal growth rates for reporting units			0.00%
Discount rates for reporting units			9.00%
Maximum [Member]
Goodwill and Intangible Assets Net [Line Items]
Long-term terminal growth rates for reporting units			3.00%
Discount rates for reporting units			13.50%
Patents [Member]
Goodwill and Intangible Assets Net [Line Items]
Gross amortizable intangible assets	39,930		$ 39,930			39,901
Less: Accumulated amortization	33,758		33,758			32,408
Finite-Lived Intangible Assets, Net	6,172		6,172			7,493
Trade Names And Trademarks [Member]
Goodwill and Intangible Assets Net [Line Items]
Gross amortizable intangible assets	43,900		43,900			40,086
Less: Accumulated amortization	26,135		26,135			24,017
Finite-Lived Intangible Assets, Net	17,765		17,765			16,069
Licensing Agreements [Member]
Goodwill and Intangible Assets Net [Line Items]
Gross amortizable intangible assets	50,983		50,983			57,767
Less: Accumulated amortization	41,111		41,111			46,507
Finite-Lived Intangible Assets, Net	9,872		9,872			11,260
Core Technology [Member]
Goodwill and Intangible Assets Net [Line Items]
Gross amortizable intangible assets	295,956		295,956			304,187
Less: Accumulated amortization	229,848		229,848			233,720
Finite-Lived Intangible Assets, Net	66,108		66,108			70,467
Customer Relationships [Member]
Goodwill and Intangible Assets Net [Line Items]
Gross amortizable intangible assets	422,291		422,291			383,303
Less: Accumulated amortization	219,052		219,052			213,062
Finite-Lived Intangible Assets, Net	203,239		203,239			170,241
In-process Research and Development [Member]
Goodwill and Intangible Assets Net [Line Items]
Gross amortizable intangible assets	84,252		84,252			78,515
Less: Accumulated amortization	4,933		4,933			4,405
Finite-Lived Intangible Assets, Net	$ 79,319		$ 79,319			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						$ 277,400